Who makes consequential choices?
Individuals, firms, states, algorithms?
The relevant player is any actor whose choice can alter outcomes.
Side 22
Game Theory
A study of decisions whose outcomes depend on other decision-makers. Game theory makes strategic interdependence explicit: players anticipate one another, information is uneven and commitments can change the game itself.
players→strategies→payoffs→information→equilibrium
05game elements
06canonical games
05strategic devices
22Side
Strategy begins when choices are interdependent.
A game is defined by who acts, what they can do, what each outcome is worth and what each player knows when choosing.
What complete plans are available?
Action or contingent plan?
A strategy can specify what to do after every possible information state.
What outcomes does each player prefer?
Money, survival, status, risk?
Payoffs encode preferences, not necessarily cash.
Who knows what, and when?
Perfect, imperfect, private?
Information structure often changes the strategic solution more than the physical action set.
Simultaneous or sequential?
Who moves first?
Being able to observe, commit or react can transform incentives.
An equilibrium is mutual strategic consistency.
It does not mean fair, efficient or desirable. It means each player’s strategy is a best response to what others are doing, under the model.
Best regardless of others.
A strategy dominates when it yields at least as good an outcome across all relevant opponent choices.
Best given others’ strategies.
Strategic reasoning often begins by asking how each player would respond to every possible opponent move.
No unilateral profitable deviation.
Each player’s chosen strategy is a best response to the others’ choices.
Randomize deliberately.
When predictability can be exploited, equilibrium may require choosing actions probabilistically.
Strategies remain credible later.
In sequential games, an equilibrium should specify rational continuation behavior after every relevant history.
No one can improve without another worsening.
Efficiency and equilibrium are different concepts and need not coincide.
Equilibrium is not endorsement.
A stable strategic outcome can be collectively wasteful, unequal or fragile.
Canonical games isolate recurring strategic tensions.
The labels are useful because similar incentive structures reappear in very different domains.
| Game | Strategic tension | Key question | Typical lesson |
|---|---|---|---|
| Prisoner’s dilemma | Private incentive vs joint welfare | Can cooperation be sustained? | Individually rational choices can produce a worse joint outcome. |
| Coordination | Several compatible equilibria | Which convention wins? | Expectations and focal points matter. |
| Chicken | Each wants the other to yield | Whose commitment is credible? | Commitment can create leverage while increasing risk. |
| Battle of the Sexes | Coordination + distribution conflict | How is the preferred equilibrium selected? | Agreement on coordination need not imply agreement on outcome. |
| Stag hunt | Safe individual option vs high-payoff cooperation | Can players trust one another? | Risk dominance can compete with payoff dominance. |
| Matching pennies | Pure conflict | How can predictability be avoided? | Randomization can be strategically necessary. |
The future can discipline the present.
Repeated interaction allows reputation, reciprocity and punishment to support behavior that would not survive in a one-shot game.
Shadow
How much does the future matter?
Cooperation is easier when players expect to interact again and value future payoffs sufficiently.
Reciprocity
Respond to behavior.
Strategies can reward cooperation and punish defection, linking current behavior to later consequences.
Reputation
Past action becomes information.
Observed history can change what others expect and therefore how they behave toward the player.
Forgiveness
Avoid endless retaliation.
Noise and mistakes can make unforgiving punishment strategies collapse into permanent conflict.
Entry/exit
Relationships can end.
The ability to leave, switch partners or exclude defectors changes the strategic environment.
Private information creates games about belief.
When players know different things, actions can reveal information intentionally or unintentionally.
Action conveys hidden type.
A signal is informative when different types have different costs or incentives to send it.
Design choices that sort types.
A less-informed actor can offer a menu that induces others to reveal private information through selection.
Manipulate beliefs.
Strategic misrepresentation can be profitable when opponents cannot directly observe the true state.
Communication without direct commitment.
Messages can still convey information when sender and receiver incentives are sufficiently aligned.
Everyone knows that everyone knows.
Coordination can depend not only on facts but on recursively shared awareness of those facts.
Reason over uncertain types.
Players choose strategies based on beliefs about private characteristics or information held by others.
Sometimes the problem is to design the game.
Mechanism design reverses the usual question: instead of asking what players will do under fixed rules, ask which rules produce desirable outcomes given strategic behavior.
Desired outcome
Define what the mechanism is trying to achieve: allocation, revenue, truth-telling, participation or efficiency.
Private information
Identify what participants know that the designer does not.
Message space
Specify what participants can report, bid, choose or reveal.
Allocation rule
Define how reported information is translated into outcomes.
Incentive compatibility
Ask whether truthful or intended behavior is actually optimal for participants.
Participation constraint
Participants must prefer joining the mechanism to their outside option.
Game TheoryFudenberg & Tirole · formal foundation
Games of StrategyDixit, Skeath & Reiley · applied introduction
Thinking StrategicallyDixit & Nalebuff · strategic reasoning
Strategy: An Introduction to Game TheoryJoel Watson · core models