Game Theory

1. Important Game Theoretical Models
   1. Prisoner's Dilemma
      1. Description
         1. Two players choose between cooperation and defection
         2. Dominant strategy is to defect, despite mutual benefit from cooperation
      2. Applications
         1. Economics: Oligopoly markets
         2. Political Science: Arms races
         3. Social Sciences: Trust issues
      3. Variations
         1. Iterated Prisoner's Dilemma
            1. Repeated interactions
            2. Possibility of strategy evolution over time
         2. Spatial Prisoner's Dilemma
            1. Players inhabit a spatial grid
            2. Influence of local interactions
      4. Resolution approaches
         1. Encouraging cooperation through repeated interactions
         2. Influencing payoffs to modify incentives
   2. Hawk-Dove (Chicken) Game
      1. Description
         1. Two players choose aggressive (hawk) or conciliatory (dove) actions
         2. Balance of risk and reward
      2. Payoff structure
         1. High payoff for one aggressor facing a conciliatory player
         2. Mutual loss from both choosing hawk
      3. Applications
         1. Animal behavior and evolutionary strategies
         2. Human conflict and negotiation scenarios
      4. Evolutionary implications
         1. Mixed population strategies
         2. Stability of peace versus aggression dynamics
   3. Battle of the Sexes
      1. Description
         1. Coordination game with multiple equilibria
         2. Players prefer similar but differing outcomes
      2. Payoff structure
         1. Higher payoff for coordinated action
         2. Importance of pre-game communication
      3. Cultural and social implications
         1. Gender dynamics in decision-making
         2. Explorations of bargaining and compromise
   4. Stag Hunt
      1. Description
         1. Cooperation vs. safety choice under risk
         2. Assurance game with trust elements
      2. Payoff implications
         1. Mutual benefit from cooperation
         2. Risk aversion leads to safer but suboptimal strategies
      3. Strategic analysis
         1. Influence of trust and social norms
         2. Evolution toward optimal cooperation
   5. Cournot and Bertrand Models
      1. Cournot Model
         1. Oligopoly model focusing on production quantities
         2. Firms decide quantities independently, impacting market prices
      2. Bertrand Model
         1. Competition focused on price setting
         2. Implications for monopoly vs. competition pricing
      3. Economic applications
         1. Market structure analysis
         2. Price vs. quantity competition effects
      4. Extensions and critiques
         1. Assumptions of rationality and market structure
         2. Real-world deviations from theoretical predictions
   6. Public Goods Game
      1. Description
         1. Voluntary contribution to public resources
         2. Dilemma of free-riding vs. collective benefit
      2. Payoff dynamics
         1. Benefits shared despite individual contribution variance
         2. Challenge of sustaining public good investment
      3. Sociopolitical implications
         1. Funding public services
         2. Environmental policy and resource management
      4. Incentive structures
         1. Mechanisms to enforce contributions
         2. Role of punishment and rewards
   7. Voting Games
      1. Description
         1. Strategic decision-making in voting contexts
         2. Influence of preferences and coalition formations
      2. Types of voting games
         1. Majoritarian systems
         2. Proportional representation
      3. Game theoretical insights
         1. Manipulation of voting outcomes
         2. Strategic candidate positioning and platform selection
      4. Real-world applications
         1. Political elections and referendums
         2. Corporate decisions in shareholder meetings