💹Business Economics Unit 7 – Game Theory & Strategic Decisions

Key Concepts in Game Theory

• Game theory analyzes strategic interactions between rational decision-makers
• Players are the individuals or groups making decisions in a game
• Strategies are the complete plans of action that players can choose
• Payoffs are the outcomes or rewards that players receive based on the strategies chosen
• Zero-sum games have a fixed total payoff that is divided among the players (Poker)
• Non-zero-sum games allow for outcomes where all players can gain or lose (Prisoner's Dilemma)
• Simultaneous games involve players making decisions at the same time without knowledge of others' choices
• Sequential games involve players making decisions in a specific order, aware of previous choices

Types of Games and Strategies

• Static games are played simultaneously, where players choose their strategies without knowing the choices of other players
• Dynamic games are played sequentially, where players take turns making decisions based on the moves of other players
• Cooperative games allow players to communicate and form binding agreements to coordinate their strategies
• Non-cooperative games do not allow for enforceable agreements, and players make independent decisions
• Pure strategies are specific actions that a player chooses to take in a game (Always confess in Prisoner's Dilemma)
• Mixed strategies involve randomly selecting among available pure strategies based on a probability distribution
• Dominant strategies are the best choice for a player regardless of the strategies chosen by other players
• Dominated strategies are those that always lead to worse payoffs compared to other available strategies

Nash Equilibrium and Its Applications

• Nash equilibrium is a state where each player's strategy is the best response to the strategies of other players
• In Nash equilibrium, no player has an incentive to unilaterally change their strategy
• Nash equilibrium can be pure (players choose specific strategies) or mixed (players randomize their strategies)
• Existence of Nash equilibrium depends on the type of game and the number of players
• Nash equilibrium helps predict the outcomes of strategic interactions in various fields (Economics, political science, psychology)
• Applications of Nash equilibrium include market competition, voting behavior, and international relations
• Nash equilibrium may not always be the most efficient or socially optimal outcome (Prisoner's Dilemma)
• Refinements of Nash equilibrium, such as subgame perfect equilibrium, address dynamic games and credible threats

Decision Trees and Extensive Form Games

• Decision trees visually represent the sequential structure of a game
• Nodes in a decision tree represent decision points for players or chance events
• Branches in a decision tree represent the available choices or outcomes at each node
• Payoffs are listed at the terminal nodes of the decision tree
• Extensive form games are represented using decision trees, capturing the order of moves and information available to players
• Backward induction is used to solve extensive form games by starting at the terminal nodes and working backwards
• Subgame perfect equilibrium is determined by finding the Nash equilibrium at each subgame (portion of the game tree)
• Extensive form games can model situations with imperfect information, where players are unaware of some previous moves

Dominant and Mixed Strategies

• Dominant strategy equilibrium occurs when each player has a dominant strategy, resulting in a Nash equilibrium
• Iterated elimination of dominated strategies can be used to simplify games and find dominant strategy equilibria
• Mixed strategy equilibrium involves players randomizing their strategies based on specific probabilities
• In a mixed strategy equilibrium, players are indifferent between their available pure strategies
• Mixed strategies can be used to exploit opponents' tendencies and avoid being predictable
• Calculating mixed strategy equilibria involves finding probabilities that make players indifferent between strategies
• Mixed strategies are common in competitive settings (Sports, poker, business competition)
• Mixed strategy equilibria may not always exist, depending on the structure of the game

Cooperative vs. Non-Cooperative Games

• Cooperative games allow players to communicate, form coalitions, and make binding agreements
• In cooperative games, players can negotiate and distribute payoffs among themselves
• Shapley value is a solution concept for cooperative games that assigns fair payoffs to players based on their marginal contributions
• Core is another solution concept that ensures no group of players has an incentive to break away from the grand coalition
• Non-cooperative games do not allow for enforceable agreements, and players make independent decisions
• In non-cooperative games, players cannot credibly commit to strategies that are not in their individual best interests
• Nash equilibrium is the primary solution concept for non-cooperative games
• Many real-world situations involve a combination of cooperative and non-cooperative elements (International treaties, business partnerships)

Game Theory in Business Contexts

• Game theory helps businesses make strategic decisions in competitive markets
• Oligopoly models, such as Cournot and Bertrand competition, analyze firm behavior in concentrated industries
• Price wars can be modeled as a Prisoner's Dilemma, where firms have incentives to undercut each other
• Product differentiation and market segmentation can be analyzed using game-theoretic frameworks
• Entry deterrence strategies, such as limit pricing and capacity expansion, can be studied using extensive form games
• Bargaining and negotiation situations, such as labor-management disputes, can be modeled using cooperative game theory
• Auctions and bidding behavior can be analyzed using game-theoretic concepts (First-price sealed-bid auction, Vickrey auction)
• Game theory helps businesses anticipate competitor moves and make strategic investments

Advanced Topics and Real-World Applications

• Repeated games involve players interacting over multiple rounds, allowing for cooperation and punishment strategies
• Evolutionary game theory studies the dynamics of strategy adoption in populations over time
• Signaling games model situations where players have private information and can send costly signals to convey their types
• Mechanism design involves creating game rules and incentives to achieve desired outcomes (Auctions, voting systems)
• Behavioral game theory incorporates insights from psychology and relaxes assumptions of perfect rationality
• Experimental game theory tests theoretical predictions using controlled laboratory experiments
• Game theory has applications in various fields beyond economics (Biology, computer science, political science)
• Real-world applications include spectrum auctions, kidney exchange programs, and climate change negotiations