Game theory is the mathematics of decisions whose consequences depend on other decision-makers’ choices. It studies not only what an individual should do, but what happens when several individuals are reasoning, anticipating and responding at the same time.
A student choosing a revision topic can sometimes treat the available choices as a personal planning problem. Two students deciding how to divide a shared project cannot do that so easily. Each student’s outcome depends partly on what the other contributes. A timetable, a shared resource, a coordination convention or a negotiation can contain the same strategic structure even when nobody calls it a game.
The subject is not a universal method for defeating people. Cooperation, coordination, credible commitments and well-designed rules are as important as competition. It is also not a claim that human beings are perfectly calculating. Game theory constructs models. The model’s players, information, available actions and preferences must be examined before its conclusions are applied.
This article develops the mathematics through small games that can be checked completely. The payoff numbers and classroom situations are illustrative, not psychological measurements or claims about how particular students behave. The goal is to see how individual reasoning can produce collective outcomes—and why an outcome that nobody changes alone may still be poor for everyone.
Series route: Mathematics Learning Hub → How Mathematics Works → Game Theory. Useful prerequisites are Probability and Mathematical Optimisation.
Reading map: What defines a game? · A complete payoff example · Equilibrium and efficiency · Randomised strategies · Sequential choices · Repeated interaction · Private information · Designing rules · Learning checks.
1. What must be specified before a game can be analysed?
A game needs players, available strategies and a rule assigning an outcome or payoff to each combination of strategies. Timing and information matter too. Does a participant choose before seeing another’s action? Are preferences known? Can an agreement be enforced? The answers determine which mathematical game has actually been defined.
Consider two people arranging a meeting. If they can speak, confirm a location and trust the confirmation, their problem differs from choosing independently without communication. If one moves first and the other observes that choice, the timing creates another game. The physical locations might be identical across all three situations while the strategic structure changes.
A good model does not begin with an elaborate payoff matrix and hope it represents the situation. It first asks which decisions interact and what each participant can observe when deciding. MIT’s Economic Applications of Game Theory separates representation, dominance, equilibrium, sequential interaction and information into distinct parts of the subject for precisely this reason.
2. An action is not always a strategy
An action is a move at a particular decision point. A strategy is a complete contingent plan: what to do at every information situation where a choice might be required. In a one-move game, the difference is small. In a sequential game, it becomes fundamental.
Suppose a project partner can either deliver a draft on time or late. Your plan might be: review the draft if it arrives on time; prepare a short replacement outline if it arrives late. That plan specifies actions for two possible situations, although only one may actually occur. The unused branch still belongs to the strategy because the other participant may anticipate it.
This matters when people make threats or promises. A statement about a future action influences the present only to the extent that others believe the action will actually be chosen when its decision point arrives. Analysing the full strategy therefore requires looking beyond the realised path.
The mathematical advantage is that a complicated sequence can be represented as a comparison among complete plans. The danger is forgetting that these plans must respect what the player knows. A strategy cannot legitimately depend on information that has not yet been observed.
3. Payoffs describe preferences, not necessarily money
A payoff is a numerical representation used to compare outcomes. It may include time, effort, enjoyment, fairness, reputation, task completion or financial consequences. Using a utility function does not require assuming that a person cares only about money or only about themselves.
For example, a student might prefer a lower individual score when it comes with an honest division of work. Another might place substantial weight on a partner’s stress. Such preferences can be represented in the model. The mathematical issue is whether the proposed payoffs capture the preferences relevant to the decision, not whether the preferences fit a stereotype of selfishness.
Care is required when comparing payoffs across people. A utility score of 8 for one player does not automatically mean twice the wellbeing represented by 4 for another. Within a player’s decision problem, utility numbers support the comparisons specified by the model. Adding different people’s utilities as though they were directly comparable requires additional assumptions.
When uncertain outcomes are involved, expected-utility calculations also require a representation suitable for those comparisons. Merely ranking certain outcomes is not enough to justify averaging arbitrary labels assigned to them.
4. A shared-project dilemma in four outcomes
Imagine two participants, Row and Column, who can contribute to a shared project or skip their contribution. The table below is a constructed game. In every cell, the first number is Row’s payoff and the second is Column’s.
| Row’s choice | Column contributes | Column skips |
|---|---|---|
| Contribute | (3, 3) | (0, 5) |
| Skip | (5, 0) | (1, 1) |
These numbers encode a particular tension. Both contributing produces a good shared result. A person who skips while the other contributes receives the benefit without the effort. When both skip, the project performs poorly, although each avoids the effort cost.
Nothing in the table says real students must have these preferences. Changing responsibility, friendship, assessment rules or the value attached to doing one’s part can change the payoffs and therefore change the game. The table is useful because it isolates a mechanism: individual incentives may point away from the jointly preferred outcome.
Before calculating anything, check that the verbal story and the table agree. Against a contributor, skipping gives 5 rather than 3. Against someone who skips, skipping gives 1 rather than 0. Those comparisons, rather than the names of the actions, will drive the conclusion.
5. Dominance removes the need to guess the other move
A strictly dominant strategy gives a player a higher payoff than every alternative against every possible strategy combination of the other players. In the shared-project table, skipping strictly dominates contributing for each participant. The comparison holds in both columns for Row and in both rows for Column.
This is stronger than saying that skipping is usually attractive or has a high average payoff. A dominance claim must survive every opponent choice included in the model. If an alternative beats skipping in even one relevant situation, strict dominance has not been established.
Dominance therefore separates some games from ordinary forecasting. A player with a strictly dominant strategy need not form a detailed probability estimate about the other player’s move to identify the preferred action. But many games have no dominant strategy. The absence of dominance does not mean reasoning stops; it means the reasoning must account for the other player’s choices or beliefs.
For the formal distinction between dominance and best responses, see MIT’s lecture on dominance. The shared-project comparisons here can be checked directly from the table.
6. Nash equilibrium is a mutual best-response condition
A Nash equilibrium is a strategy profile in which no player can improve their payoff by changing their own strategy alone while the others’ strategies remain fixed. The condition is unilateral. It does not test every coordinated change by several participants. MIT’s Nash equilibrium lecture develops this mutual best-response idea.
In the shared-project game, both skipping is the equilibrium. Starting there, Row would reduce their payoff from 1 to 0 by contributing alone. Column faces the same comparison. Neither benefits from a unilateral switch.
Both contributing is not an equilibrium under these particular payoffs. With Column contributing, Row can increase their payoff from 3 to 5 by skipping. The same temptation exists for Column. The jointly attractive cell does not contain its own incentive to remain there.
This is the central distinction between wishing for an outcome and explaining how that outcome sustains itself. An equilibrium condition asks whether the individual choices support one another once the whole profile is specified. It does not certify that the profile is kind, wise, fair or desirable.
7. Equilibrium is not collective efficiency
In the project table, both players receive 3 when both contribute and only 1 when both skip. Both would prefer the coordinated change from skipping to contributing. Yet neither wants to make that change alone. The equilibrium is therefore Pareto dominated by another feasible outcome.
This observation is not a paradox. The equilibrium test and the efficiency test ask different questions. Equilibrium asks whether an individual can gain from a unilateral deviation. Pareto comparison asks whether a different outcome can improve somebody without harming anybody else. A coordinated improvement can exist even when unilateral improvements do not.
The distinction matters for institutional design. Telling participants to “choose rationally” may not produce the intended collective result when the rules reward free-riding. Repair might require a different assessment structure, verifiable commitments or a better division of responsibility. Each repair changes some part of the game.
The related Mathematical Optimisation article studies a single declared objective. Game theory asks what happens when separate objectives interact. A system of individual optimisers is not automatically one optimiser acting for everybody.
8. Coordination games can have several equilibria
Now consider two teams choosing a shared file format, A or B. If both choose A, each receives payoff 4. If both choose B, each receives 3. If they choose different formats, each receives 0 because the files cannot be combined within the simplified model.
Both choosing A is an equilibrium: either team would lose by switching alone. Both choosing B is also an equilibrium for the same reason. Neither strategy is dominant, because the best choice depends on what the other team chooses.
This creates an equilibrium-selection problem. Knowing that an equilibrium exists does not tell us which convention will be adopted. Communication, an established default or a trusted coordinator may help align expectations. These mechanisms need not change the intrinsic value of the formats; they can change the information each team has about the other’s intended action.
The example also explains why replacing an inferior convention can be difficult. A jointly beneficial switch requires coordination. One team adopting the preferred standard alone may initially make matters worse. The path from one equilibrium to another is a separate problem from ranking their payoffs.
9. Best responses depend on beliefs when choices are uncertain
Suppose Row believes Column will choose format A with probability q. Choosing A gives expected payoff 4q. Choosing B gives expected payoff 3(1−q). Row prefers A when 4q≥3(1−q), or q≥3/7.
This calculation shows exactly where a belief changes the best response. If Row thinks the other team is very likely to use A, A is attractive. If B is sufficiently more likely, B becomes the better response despite A being the better coordinated convention.
The calculation is conditional, not a psychological prediction. We have not measured q. We have shown what follows from each possible q under the specified utilities. That distinction is valuable: the mathematical model can identify the information needed for a recommendation even when that information has not been supplied.
At q=3/7, the player is indifferent between the two choices. Indifference thresholds will become important in mixed strategies because randomisation can be sustained only when the opponent’s choices make the actions in use equally attractive.
10. Mixed strategies are probability distributions over plans
A pure strategy selects one plan with certainty. A mixed strategy assigns probabilities to pure strategies. Randomisation can be strategically meaningful when predictability itself creates a disadvantage. The university resource EconPort’s mixed-strategy explanation uses matching pennies to demonstrate the principle.
Take a two-choice matching game. Row receives +1 if both players choose the same symbol and −1 if they choose different symbols. Column receives the opposite payoff. If Row always chooses the first symbol, Column can always choose the second. If Column always chooses the second, Row can match it. No pair of fixed pure actions is stable against unilateral change.
Now let each player choose each symbol independently with probability one half. Against Column’s mixture, either pure action gives Row expected payoff zero. Column has the same property. Neither can improve by switching to a different distribution. That is a mixed-strategy equilibrium.
The lesson is not “always be unpredictable.” Randomisation is useful because of this game’s payoff structure. In a coordination game, independent random choices may create avoidable mismatches. The correct role of uncertainty depends on the game.
11. Solving a mixed equilibrium through indifference
Change Row’s matching-game payoffs to the following matrix; Column still receives their negatives. Matching the first symbol pays Row 2, while matching the second pays 1.
| Row’s action | Column: first | Column: second |
|---|---|---|
| First | 2 | −1 |
| Second | −1 | 1 |
If Column chooses first with probability q, Row’s expected payoff from first is 2q−(1−q)=3q−1. From second it is −q+(1−q)=1−2q. Indifference requires 3q−1=1−2q, so q=2/5.
If Row chooses first with probability p, Row’s expected payoff against Column’s first is 3p−1 and against Column’s second is 1−2p. Column wants to minimise Row’s payoff. Making Column indifferent requires p=2/5. At these probabilities the value to Row is 1/5.
We have derived the probabilities from the payoffs. A fifty–fifty rule would not be the equilibrium of this modified game. The calculation also shows why we solve for a player’s mixture by examining the incentives it creates for the other player.
12. Zero-sum is a structural assumption, not a description of all life
A zero-sum model gives one player exactly the negative of another player’s payoff. The matching game has this structure. A shared project usually does not: both participants can gain from a successful outcome or lose from a failed one.
Calling a situation zero-sum therefore makes a strong claim about the available outcomes. It excludes the possibility of increasing or reducing the total represented payoff. Before applying competitive reasoning, ask whether cooperation can change the size of the benefit rather than merely redistribute it.
Even where one narrow metric is fixed, the whole situation may not be. Two teams competing for one award cannot both win that award, but they may both gain skills, relationships and useful work. A model focused only on the award may be appropriate for one question and misleading for another.
For learning purposes, zero-sum games are valuable because they make conflicting incentives easy to inspect. Their clarity should not be mistaken for universality. The first task remains choosing the right model, not forcing every interaction into the same one.
13. Sequential games require reasoning backwards
Suppose one team decides whether to propose a joint event. If no proposal is made, both receive 0. If a proposal is made, the second team decides whether to participate. Participation gives payoffs (3,2); rejection gives (−1,0), reflecting wasted preparation by the first team.
Reason from the second decision. Once a proposal exists, the second team prefers participation because 2 is greater than 0. Anticipating that response, the first team prefers proposing because 3 is greater than 0. This is backward induction in a small finite game with observed actions.
The result depends on the information and payoffs. If the second team has an unobserved participation cost, the first team may not know whether the response will be favourable. If the proposal cannot be withdrawn, its timing matters. If both teams decide simultaneously, the game tree no longer represents the same decision process.
Backward reasoning is not mind-reading. It applies a stated decision rule at later stages and traces its implications for earlier choices. The challenge is ensuring that later-stage assumptions are credible rather than merely convenient for the desired conclusion.
14. Credible commitments must survive the moment of action
A threat can influence another player only when its eventual execution is believable. If carrying it out would be worse for the threatening player than abandoning it, the threat may fail to support a sequentially rational outcome.
Subgame-perfect equilibrium requires strategies to form a Nash equilibrium in every subgame, not only in the full game. This rules out some outcomes sustained by non-credible behaviour off the realised path. The definition and examples are developed in MIT’s subgame-perfect equilibrium lecture.
A commitment device changes the options available later. A publicly agreed allocation rule, a deposited contribution or an automatic scheduling constraint can make a promised action more credible. But commitment can also lock people into a poor response when conditions change. The mathematics does not say that irreversible promises are always good; it shows how changing future flexibility changes present incentives.
This creates a useful planning question: are we relying on an action someone would choose voluntarily at the relevant future stage, or on a promise that becomes unattractive when that stage arrives?
15. Repetition connects today’s choice to tomorrow’s relationship
The one-shot project dilemma can change when the same participants expect to interact again. An action now affects not only the current payoff but also future cooperation. A strategy can condition later behaviour on earlier contributions.
That does not guarantee cooperation. Participants must care sufficiently about future outcomes, observe relevant behaviour reliably and have future actions capable of changing incentives. The formal repeated-game literature contains a variety of results under different monitoring and payoff assumptions. MIT’s folk-theorem lecture introduces how repeated interaction can sustain outcomes unavailable as one-shot equilibria.
A finite horizon also matters. If everyone knows the precise last interaction and the stage game has a unique equilibrium, backward reasoning can remove some simple arguments for cooperation. If the relationship may continue, the incentive structure differs. Informal statements such as “They will cooperate because they meet often” leave out the conditions that make the reasoning work.
The important mathematical change is that a strategy becomes a rule over histories. The game is no longer just one table repeated mechanically; it contains contingent responses across time.
16. A repeated-game calculation with an explicit threshold
Use the project payoffs again and assume an indefinitely repeated game with perfect observation. Let future payoffs be multiplied by a discount factor δ, where 0<δ<1. Consider a strategy that contributes while everyone has contributed previously and switches permanently to skipping after a deviation.
Remaining on the cooperative path gives 3+3δ+3δ²+…=3/(1−δ). A one-time deviation gives 5 now, followed by payoff 1 in every future period: 5+δ/(1−δ). Cooperation is preferred when 3/(1−δ)≥5+δ/(1−δ).
Multiplying by the positive quantity 1−δ gives 3≥5−4δ, so δ≥1/2. At equality the player is indifferent; above it the future loss outweighs the immediate gain. During the punishment phase, skipping remains a best response because it is dominant in the stage game.
This is a theorem about the constructed model, not advice to punish real students permanently. Noise, misunderstandings, forgiveness, changing circumstances and welfare can make such a rule unsuitable in human relationships. The calculation isolates the incentive mechanism: an immediate advantage can be outweighed by a sufficiently important future consequence.
17. Private information changes what a strategy can depend on
In many games, a participant knows something others do not: their effort cost, available time, valuation or intended response. A Bayesian game represents such private information through types and beliefs. A strategy specifies an action for each type a player might have.
Suppose participation in the joint event gives a benefit of 4, but the second team privately faces either a cost of 1 or a cost of 5. Participation is attractive for the first type and unattractive for the second. The proposing team’s expected payoff depends on its belief about which type it faces.
The model must distinguish an actual type from another player’s belief about that type. It must also prevent the proposing team from using the private cost as though it were observable. A plan that selects an action based on hidden information is not implementable without an information-gathering or communication mechanism.
For a formal treatment, see MIT’s Bayesian games notes. The broader connection is to probability: uncertainty now concerns other decision-makers, whose behaviour also depends on what they know.
18. A message is useful only through the incentives around it
Imagine a participant saying, “This task is very costly for me.” The receiver needs to know whether the statement changes beliefs. If every possible type benefits from making the same statement, the message may reveal little. If different types have different incentives to send it, the message can become informative.
This does not mean speech is generally untrustworthy. It means a model of communication should examine why a sender would reveal information accurately, selectively or not at all. Shared objectives, verifiable records and aligned incentives can support useful communication. Conflicting interests can complicate it.
A signal can also be an action rather than a sentence. Completing a small task may reveal available capacity. But the signal’s meaning depends on what it costs different types and whether it can be imitated. The observed action and the hidden quality are not automatically equivalent.
The Information Theory route measures statistical uncertainty and information. Game theory adds the question of why a strategic sender generated the observation in the first place.
19. Mechanism design works backwards from the desired outcome
Ordinary game analysis starts with rules and asks what participants may do. Mechanism design asks which rules would make desired behaviour compatible with participants’ incentives and information.
Suppose an organiser wants participants to reveal how much a scarce opportunity matters to them. Simply asking for the largest number may invite exaggeration if the allocation rewards larger reports at no cost. The reporting rule and consequence must be analysed together. A request for honesty is not itself an incentive-compatibility proof.
A familiar formal illustration is a single-item second-price auction under private values and the usual payoff assumptions. Fix the highest competing bid at b. Reporting one’s value v wins precisely when v exceeds b. If b<v, winning gives a nonnegative surplus; if b>v, winning would be worse than losing. Moving the bid away from v can create an unwanted loss or an unwanted win but cannot improve the price paid when the allocation remains unchanged.
This is an abstract incentive argument, not purchasing advice. Assumptions about private values, participation costs, externalities and constraints matter. See MIT’s auctions lecture for the distinction between first-price and second-price formats.
20. Fairness, efficiency and stability can pull in different directions
An allocation rule may be efficient under one objective but distribute benefits unevenly. Another may look fair but give participants an incentive to misreport information. A third may be stable against individual deviations while remaining collectively disappointing.
These are distinct properties. Before claiming that a mechanism is successful, name which properties have been established. Does everyone receive the same amount? Do people prefer their assigned outcome to some alternative? Can anyone improve by reporting a false preference? Can a coalition gain by coordinating a deviation? Different questions require different tests.
Consider dividing a shared resource equally. Equal division is easy to explain, but it may not reflect different needs or different uses. Allocating according to reported need may improve responsiveness while creating reporting incentives. Neither observation settles the policy. It reveals which additional values and verification mechanisms must be discussed.
Game theory is most useful here when it makes trade-offs explicit rather than using “rational” as a substitute for ethical argument. A mathematical equilibrium describes incentives under a model. It does not remove responsibility for choosing the rules.
21. Congestion shows why individually sensible choices interact
Suppose two travellers choose routes A or B. Route A takes three minutes when used by one traveller and ten minutes when both use it. Route B takes six minutes regardless. Each traveller wants to minimise their own time.
If both choose A, either can improve by moving to B, reducing their time from ten to six. If both choose B, either can improve by moving to the empty A, reducing six to three. When they split, the A traveller would worsen their time by moving to B, and the B traveller would worsen theirs by joining A. Both split allocations are equilibria.
The best route is not a permanent label. It depends on how many others use it. A recommendation based on an empty route can become inaccurate after it changes behaviour. The act of choosing affects the environment being evaluated.
This constructed example links Graph Theory, optimisation and strategic interaction. A graph supplies routes, a cost model supplies travel times, and a game describes how independent users respond. None of those layers can simply replace the others.
22. Equilibrium existence does not explain the path to equilibrium
An equilibrium is a configuration. A learning process is a rule for changing configurations over time. Even when a game has an equilibrium, a particular update rule may cycle, converge slowly or move somewhere else.
In the route example, imagine both travellers update simultaneously. After both choose A and experience ten minutes, both switch to B. After both choose B, both see that an empty A would take three minutes and switch back. The synchronous process can alternate, although split equilibria exist.
Allowing one traveller to update at a time produces a different path. Starting from both on A, one switches to B and the resulting split is stable. The equilibrium set has not changed; the adjustment process has.
This is the connection to Dynamical Systems. A complete explanation may need both a solution concept and a model of adaptation. Saying “the system will reach equilibrium” requires more than identifying a point that satisfies equilibrium equations.
23. Modelling human behaviour requires humility
People can misunderstand a game, use habits, care about unmodelled consequences or lack time for exhaustive calculation. An equilibrium prediction can fail because the payoff model is wrong, the information assumptions are wrong or the proposed reasoning process is not a good description of behaviour.
This does not make the model useless. A simplified model can still identify an incentive conflict or explain why a rule encourages a particular response. But descriptive claims need evidence. One cannot infer a person’s motives merely because their action fits one cell of a payoff matrix.
For educational use, a sensible approach is to treat the game as a hypothesis-generating structure. Ask which observable change would distinguish two explanations. Would behaviour change if contributions became visible? If the task repeated? If the payoff to helping increased? These variations clarify what the model actually assumes.
Do not turn a student’s temporary response into an identity such as “free-rider” or “irrational person.” The mathematical object is a decision under stated conditions. The human being is larger than the model.
24. Learning checks: reconstruct the incentives
Check one: In the original project game, why is both contributing not an equilibrium? Hold one player’s action fixed at contributing. The other receives 5 by skipping rather than 3 by contributing. A unilateral improvement exists. A statement about what both players should do together does not answer that test.
Check two: In the format game, why is B still an equilibrium when A gives a better coordinated payoff? Starting from both on B, one team switching alone produces a mismatch and reduces its payoff from 3 to 0. Equilibrium tests unilateral changes from the specified profile, not coordinated moves to every better profile.
Check three: In the asymmetric matching game, what makes two-fifths the correct mixing probability? It equalises the opponent’s payoff from the actions that remain in use. Substituting the probability into the two expected-payoff expressions verifies the equality. Guessing equal probabilities would ignore the changed reward of 2.
Check four: Why can the route-choice update cycle even though equilibria exist? Because both travellers respond to the old state simultaneously. The update rule changes the state in a way neither considered while treating the other’s action as fixed. Equilibrium and adjustment dynamics are different objects.
A strong learner should be able to explain these answers without relying on the words “Nash,” “dominance” or “mixed strategy” alone. The terms are useful labels after the mechanism is understood.
25. Common questions about game theory
Does game theory assume everyone is selfish?
No. A utility model can include concern for others, honesty, identity, fairness and shared success. What matters is that the model states the relevant preferences accurately enough for the question. Maximising a utility function does not, by itself, specify what the person values.
Is an equilibrium necessarily unique?
No. The format-coordination game has at least the two pure equilibria described above. Multiple equilibria create questions about conventions, beliefs and selection. Finding one equilibrium does not prove that all participants must coordinate on it.
Is randomisation the same as indecision?
No. A mixed strategy is a specified probability distribution. It can be a carefully chosen response to the cost of predictability. Indecision may not specify any stable distribution or reasoning at all. Whether deliberate randomisation helps depends on the game’s payoff structure.
Can communication solve every coordination problem?
No. Communication can align beliefs when messages are understood and incentives support their use. It may do little when participants benefit from misleading one another, cannot verify promises or face conflicting objectives that communication alone does not change. A message and an enforceable agreement are not the same thing.
Why study games when real life is more complicated?
Small games make one mechanism visible at a time. The lesson is transferable when the same incentive and information structure appears elsewhere. The transfer fails when a superficial resemblance replaces a careful check of players, actions, payoffs and timing.
26. The deeper idea: a decision changes another decision
The ordinary optimisation question is: given the environment, which choice is best? The game-theoretic question adds a loop: other participants choose too, their choices affect mine, and my choice may affect what they expect or do next.
That loop explains why cooperation can fail despite shared benefits, why conventions can persist despite better alternatives, why randomisation can become a strategy, and why a rule that looks fair on paper can encourage inaccurate reporting. It also explains why thoughtful institutional design can make cooperation easier rather than relying entirely on goodwill.
A reliable analysis moves from the real interaction to a declared game, from the game to best responses, from best responses to an appropriate solution concept, and then back to the original people and purpose. At the return stage, ask what the model omitted and whether the predicted behaviour has actually been observed.
Game theory makes strategic interdependence visible. Its value is not reducing people to numbers. It is showing where the structure of an interaction supports a good outcome, where it undermines one, and which changes to information or incentives would alter the result.
Sources and further study
Primary teaching sources include MIT’s lectures on dominance, Nash equilibrium, subgame-perfect equilibrium, repeated games and auctions; MIT’s Bayesian games notes; and Georgia State University’s EconPort explanation of mixed strategies. The worked payoff calculations above are educational models with explicitly stated assumptions.
How Mathematics Works | Batch 07
Mathematical Optimisation studies best feasible choices. Game Theory studies their interaction. Information Theory studies uncertainty and communication. Dynamical Systems studies the paths produced when decisions and states keep changing.
Return to the Mathematics Learning Hub or the How Mathematics Works root.