Game Theory — Nov 30, 2024

• Ways of analyzing strategic situations. Every decision you make exists within a complex web of interactions, where your success depends not just on your choices, but on the choices of others. This fundamental insight forms the backbone of game theory - a mathematical framework for understanding strategic behavior.
• The essence of game theory lies in understanding that outcomes you care about do not depend solely on your actions, but also on the actions of others. This interdependence creates a fascinating dynamic where optimal strategies must account for not just what you want to do, but what you expect others to do in response.
• In game theory, dominance arguments refer to strategies that consistently outperform others. A dominant strategy yields higher payoffs regardless of opponents' choices, making it the optimal play. Conversely, a dominated strategy is always inferior to alternatives, making it rational to eliminate it from consideration. This framework is crucial in predicting outcomes in scenarios like the Prisoner's Dilemma.
• The Prisoner's Dilemma illustrates how individual rational choices can lead to collectively suboptimal outcomes. When two suspects face the choice to cooperate or betray, the dominant strategy of betrayal leads to a worse outcome for both than if they had cooperated. This paradox exemplifies how strategic thinking can sometimes conflict with collective benefit.
• Backward induction reveals optimal strategies by reasoning from the end state. Like a chess master visualizing the endgame, this method helps players identify the best moves at each decision point, assuming rational behavior from all participants. It's a powerful tool for understanding sequential games and making better strategic decisions.
• Not to go down swinging; the point is to win the game before it starts.