Rationality Assumption

Game Theory · Axiom Academy

Unit 1 - Introduction to Game Theory 1. What Does It Mean to Be "Rational"? Have well-defined preferences over outcomes Choose actions that maximize their expected payoff Use all available information effectively Apply logical reasoning to strategic decisions Rationality does not mean players are selfish, emotionless, or perfect calculators. It simply means they consistently pursue whatever goals they have, whether that's profit, fairness, revenge, or altruism. 2. Players Maximize Their Own Payoffs Given a set of available actions, a rational player chooses the action that yields the highest expected payoff. This is the optimization principle at the heart of game theory. Mathematically, if a player has a set of actions A and a payoff function u , they choose: 3. Players Have Consistent Preferences Rationality requires that preferences be transitive and complete : These axioms prevent circular preferences and ensure that players can make coherent choices. Without them, we couldn't predict behavior. 4. The Role of Rationality in Game Theory Predictions The rationality assumption allows us to make precise predictions about strategic behavior. Key concepts that depend on rationality include: Dominant Strategy: A rational player will always play a dominant strategy if one exists Nash Equilibrium: Predicts outcomes when all players are rational and expect others to be rational Backward Induction: Rational players can "solve" sequential games by reasoning backward from the end

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