Game theory offers powerful tools for analyzing strategic interactions in business. From simultaneous moves to sequential decisions, zero-sum to non-zero-sum scenarios, it covers a wide range of competitive and cooperative situations. Understanding these game types helps predict outcomes and develop effective strategies.

Real-world applications abound, from auctions and negotiations to oligopoly competition and entry deterrence. By applying game theory concepts, businesses can make informed decisions, anticipate competitor actions, and optimize their strategies in various market scenarios.

Types of Games

Simultaneous vs sequential games

• Simultaneous games involve players making decisions at the same time without knowledge of the other players' choices (Prisoner's Dilemma, Rock-Paper-Scissors)
  • Strategies are chosen independently and simultaneously
  • Payoffs depend on the combination of all players' strategies
  • Represented by normal form games using payoff matrices
• Sequential games have players making decisions in a specific order with later players aware of earlier players' actions (Stackelberg competition, Ultimatum game)
  • Players take turns making decisions
  • Strategies are chosen based on the observed actions of previous players
  • Represented by extensive form games using decision trees
  • Allows for the possibility of first-mover advantage or disadvantage

Zero-sum vs non-zero-sum games

• Zero-sum games have the total payoff for all players summing to zero, meaning one player's gain equals another player's loss (Matching Pennies, Poker)
  • Purely competitive games with no potential for mutual benefit
  • Minimax and maximin strategies are common solution concepts
  • Mixed strategies often play a crucial role in equilibrium analysis
• Non-zero-sum games do not require the total payoff to sum to zero, allowing for cooperation or mutual benefit among players (Battle of the Sexes, Stag Hunt)
  • Payoffs can be positive or negative for all players simultaneously
  • Nash equilibrium is a common solution concept
  • Pareto optimality and social welfare are important considerations
  • Coordination and cooperation can lead to better outcomes for all players

Game theory in real-world applications

• Auctions utilize game theory to analyze bidding strategies and outcomes
  1. First-price sealed-bid auction: Each bidder submits a sealed bid, with the highest bidder winning and paying their bid amount
  2. Second-price sealed-bid auction (Vickrey auction): The highest bidder wins but pays the second-highest bid amount, encouraging truthful bidding
  3. English auction: An open-outcry ascending price auction where the highest bidder wins and pays their final bid price
  4. Dutch auction: An open-outcry descending price auction where the first bidder to accept the current price wins and pays that price
• Negotiations involve game-theoretic concepts to model bargaining and decision-making
  • Bargaining games, such as the Ultimatum game or Nash bargaining solution, analyze how players divide a surplus
  • Repeated games, like the Iterated Prisoner's Dilemma, allow for the emergence of cooperation or punishment strategies (Tit-for-Tat)
  • Threat points, outside options, and bargaining power shape negotiation outcomes
  • Asymmetric information and signaling can influence negotiation strategies and results

Game outcomes in business contexts

• Oligopoly competition models the strategic interaction among a small number of firms in a market
  • Cournot competition: Firms simultaneously choose quantities, with the market price determined by the total quantity supplied
  • Bertrand competition: Firms simultaneously choose prices, with consumers buying from the firm offering the lowest price
  • Stackelberg competition: A leader firm moves first, followed by follower firms reacting to the leader's decision
• Entry deterrence strategies aim to prevent potential competitors from entering a market
  • Incumbent firms may engage in capacity expansion, predatory pricing, or limit pricing to deter entry
  • Credible threats and commitment play a crucial role in the effectiveness of entry deterrence
• Signaling games model situations where one player has private information and can send signals to other players
  • Job market signaling: Employers use education as a signal of a candidate's ability or productivity
  • Advertising: Firms use advertising expenditure as a signal of product quality to consumers
  • Warranty offers: Longer warranties can signal higher product reliability and durability
  • Screening: Uninformed players design contracts or mechanisms to induce informed players to reveal their private information (insurance markets, auctions with private values)