Assurance Game Theory

Assurance Game Theory – Strategic managerial decisions: characterized by interactive charges where managers must clearly consider the actions that their competitors may take in response to their decisions.

Interactive: when the outcome of the manager’s decision depends on the manager’s own actions and the actions of others, there is no unconditionally optimal strategy in game theory; The best of the strategy depends on the situation in which it is implemented.

Assurance Game Theory

Assurance Game Theory

4 Strategic Fundamentals Every game theory model is defined by five parameters. 1. Players: Players are entities that make decisions; The model describes the number and identity of the players. 2. Deterministic Strategy: A non-zero-probability action consists of a set of possible strategies.

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5 Strategic Fundamentals Every game theory model is defined by five parameters. (Continued) 3. Outcome or Outcome: The possible strategies of all players intersect to determine the outcome matrix. 4. Payout: Each outcome has a fixed reward for each player. The player is hypothetical, that is, wants a higher payout than a lower one. 5. Sequence of play: Play can be simultaneous or non-simultaneous, that is sequencing.

Matrix Form: A form that summarizes all possible outcomes Extensive Form: A form that provides a road map of the player’s decisions Game Tree: A game tree is another name for a broad form game and is similar to a decision tree.

Example Figure 11.1: Simultaneous Two-Person Game Figure 11.2: Allied-Barkley Pricing: Sequential Figure 11.3: Allied-Hisgl Pricing: Using simultaneous data sets to use a wide range of models to represent simultaneous decisions.

The key to solving game theory problems is the expectation of other people’s behavior. Equilibrium Equilibrium: When no player has an incentive to unilaterally change his strategy, no player can improve his payoff by unilaterally changing his strategy.

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13 Dominant Strategy Dominant Strategy: A strategy that has a higher payoff than other possible strategies The best strategy regardless of the strategy chosen by the opponent Example: Dominant Strategy Figure 11.1: A two-player game at the same time Barkley has a strongest point. strategy, which is to maintain the current level of spending. The coalition has a dominant strategy, which is to increase spending.

Figure 11.4: Matrix representation of Figure 11.2 Barkley has a dominant strategy, which is to charge $1.00. This strategy will under no circumstances give more returns than any other possible strategy. Allied has two main strategies, removing Barkley’s price of $1.00. These are $0.95 and $1.30. Figure 11.5: Iterative Dominance shows the strategic elimination of dominance.

17 NASH Equilibrium Assuming that all players are rational, each player should choose the best strategy with respect to all other players doing the same.

Assurance Game Theory

Each N player chooses a strategy si*, where i = 1, 2, 3, N. The outcome of the game is represented as an array of strategies s* = (s1*, s2*, sN*). The payoff to player i when s* is chosen is B(s*). A Nash equilibrium is an array of strategies such that Bi(s1*, s2*, sN*)  Bi(s1′, s2*, sN*) for each outcome. There is no better variety of strategy s* for any player. This balance is reasonable, optimal and stable.

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Definition of strategic foresight: the ability of managers to make rational decisions today as expected in the future Establishing backward: used in game theory to solve games by looking into the future, determining which strategic players will choose (expectations), and then choose. Act rationally, based on those beliefs In a sequential game, settling backwards means starting with the last decision in the sequence and then working back to the first decision, deciding on the best overall decision.

Example Figure 11.8: Allied-Barkley Expansion Decision Setback and the Centipede The Centipede Game: A sequential game consisting of six decisions that show the advantages of setting back in strategic thinking The best solution is for the first player to bring r game over immediately. .

Reliability of a reliable commitment: When the cost of a false commitment exceeds the relative benefits.

Credibility Commitment (continued) Example Figure 11.10: Does Barkley have a credible threat? It was not in Barkley’s interest to lower prices in response to Allied price cuts. Threats to do so are not credible. Subgames: A part of a larger game picture has three subgames and each is in equilibrium at the optimal solution, meaning that the equilibrium is a perfect balance of the subgames.

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Allied and Barkley produce similar products and have similar cost structures. Each player must decide whether to bid high or low. Figure 11.11: Pricing as a Solution to the Prisoner’s Dilemma Given the two low prices. Both would be better if both were priced high.

Repeated play can lead to cooperative behavior in a prisoner puzzle game. Trust, reputation, promises, threats and revenge are only relevant if play happens repeatedly. Cooperative behavior is more likely if there is an infinite time horizon than if there were a limited time horizon. If there is a limited time frame, then the value of cooperation, and therefore the possibility of it, decreases when the time frame is close. Internal setup means that cooperation will not occur in this case.

Folk theory: any type of behavior can be supported by equilibrium (as long as the player believes there is a high probability of future interactions).

Assurance Game Theory

Incomplete Information Games (IIG): A branch of game theory that relaxes the restrictive assumption that all players have the same information. Asymmetric information is concentrated in the categories of players. The category has features unknown to other players who prefer (pay) different pages. Low price and hard type high price and soft type

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Example Figure 11.12: Hard or soft Barkley managers If Barkley managers were hard, they would fight, and Allied would not enter the market. If the manager Barkley is gentle, he will not fight, and will enter the market. Tit for tat: a strategy where the players cooperate in the first stage and in the successful stage each player imitates the strategy of other players in the previous stage.

A good reputation requires a schedule and incomplete information. Reputation is based on a history of player behavior and involves predicting future behavior based on past behavior.

37 Coordination Games Coordination games have more than one Nash equilibrium and the player’s problem is which one to choose. A matching game with two Nash equilibria Coordination problems arise from the inability of players to communicate, players with different strategic styles, and asymmetric information.

Figure 11.13: Product coordination The Nash equilibrium game is for one company to produce for the industrial market and another to produce for the consumer market. Both companies want a balance with higher wages.

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Players prefer different balances. Figure 11.14: Battle of the Sexes The Nash Equilibrium is for one to produce the high end and the other to produce the low end. Both players prefer to produce high-end products.

Outcome 12, 12 is Pareto dominant, because both players are better off, but has the risk of being dominated because if one firm decides to switch and the other doesn’t, then the player who switched gets a profit of zero. Achieving a Pareto-dominated solution requires cooperation and trust, due to the risk of nullification.

Players prefer different balances. First Mover Advantage Figure A Nash Equilibrium is for one firm to produce a superior product and another firm to produce an inferior product. Both companies want to produce better products, which provide higher returns, by moving first. Barkley is expected to move first because the salary is higher for Barkley and therefore Barkley can pay more to speed up the development.

Assurance Game Theory

Nash Equilibria Two players prefer different equilibria. Figure 11.17: The Hawk and the Pigeons The Nash Equilibrium means that one behaves like a dove and the other behaves like a dove. Both players want to act like a hawk, which gives a higher profit. If both players act like hawks, a clash occurs.

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Zero-sum games: A competitive game where a win by one player means a loss by another player Figure 11.18: The Campaign Nash Equilibrium is for Barkley to choose campaign 2 and for the league to choose campaign A.

To make this website work, we record user data and share it with processors. In order to use this website, you must agree to our privacy policy, including our cookies policy. Dilemma Game Row Player: Dominant Strategy: Fink Column Player: Dominant Strategy: Fink Dominant Strategy (Nash) Balance: (-8, -8) Note: It is difficult since then if they both cooperated by waiting silent: (-1, – 1). -1 -10 -8

The Prisoner’s Dilemma game can occur in many contexts: what is best for the individual may not be what is best for the department; What is best for the department may not be what is best for the company; What is best for many companies is not best for the industry; What is best for the industry may not be what is best for the nation; And what

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