Game Theory

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Game Theory

  1. 1. Game Theory and Strategic Behavior
  2. 2. <ul><li>Developed in 1950s by mathematicians John von Neumann and economist Oskar Morgenstern </li></ul><ul><li>Designed to evaluate situations where individuals and organizations can have conflicting objectives </li></ul>
  3. 3. <ul><li>Any situation with two or more people requiring decision making can be called a game. </li></ul><ul><li>A game is a description of strategic interaction that includes the constraints on the actions that the players can take and the players’ interests, but does not specify the actions that players do take. </li></ul><ul><li>A strategy is a course of action taken by one of the participants in a game </li></ul><ul><li>Payoff is the result or outcome of the strategy </li></ul><ul><li>Game theory is about choices (finite). While game theory cannot often determine the best possible strategy, it can determine whether there exists one. </li></ul><ul><li>Game theorists may assume players always act in a way to directly maximize their wins (the Homo economicus model) </li></ul>
  4. 4. <ul><li>Objective – Increase profits by price change </li></ul><ul><li>Strategies </li></ul><ul><li>Maintain prices at the present level </li></ul><ul><li>Increase prices </li></ul><ul><li>Above matrix shows the outcomes or payoffs that result from each combination of strategies adopted by the two participants in the game </li></ul>No Price Change Price Increase No Price Change Price Increase Firm 2 Firm 1 10, 10 100, -30 -20, 30 140, 35
  5. 5. <ul><li>Defined as a set of strategies such that none of the participants in the game can improve their payoff, given the strategies of the other participants. </li></ul><ul><li>Identify equilibrium conditions where the rates of output allowed the firms to maximize profits and hence no need to change. </li></ul><ul><li>No price change is an equilibrium because neither firm can benefit by increasing its prices if the other firm does not </li></ul>
  6. 6. <ul><li>For some games, there may be no Nash equilibrium; continuously switch from one strategy to another </li></ul><ul><li>There can be more than one equilibrium </li></ul>Firm 2 Firm 1 No Price Change No Price Change Price Increase Price Increase Both firms increasing their price is also a Nash equilibrium 10, 10 100, -30 -20, 30 140, 25
  7. 7. <ul><li>One firm’s best strategy may not depend on the choice made by the other participants in the game </li></ul><ul><li>Leads to Nash equilibrium because the player will use the dominant strategy and the other will respond with its best alternative </li></ul><ul><li>Firm 2’s dominant strategy is not to change price regardless of what Firm 1 does </li></ul>
  8. 8. <ul><li>An alternative that yields a lower payoff than some other strategies </li></ul><ul><li>a strategy is dominated if it is always better to play some other strategy, regardless of what opponents may do </li></ul><ul><li>It simplifies the game because they are options available to players which may be safely discarded as a result of being strictly inferior to other options. </li></ul>
  9. 9. <ul><li>A strategy s¡ in set S is strictly dominated for </li></ul><ul><li>player i if there exists another strategy, s¡’ in S such that, </li></ul><ul><li>Π i(s¡’) > Π i(s¡) </li></ul><ul><li>In this case, we say that s¡’ strictly dominates s¡ </li></ul><ul><li>In the previous example for Firm 2 no price change is a dominant strategy and price change is a dominated strategy </li></ul>
  10. 10. <ul><li>Highly competitive situations (oligopoly) </li></ul><ul><li>Risk-averse strategy – worst possible outcome is as beneficial as possible, regardless of other players </li></ul><ul><li>Select option that maximizes the minimum possible profit </li></ul>
  11. 11. <ul><li>Each firm first determines the minimum profit that could result from each strategy </li></ul><ul><li>Second, selects the maximum of the minimums </li></ul><ul><li>Hence, neither firm should introduce a new product because guaranteed a profit of at least $3 million </li></ul><ul><li>Maximin outcome not Nash equilibrium- loss avoidance rather than profit maximization </li></ul>Firm 1 Firm 2 Firm 2 Minimum Firm 1 Minimum New Product No New Product No New Product New Product 3 2 2 3 4, 4 3, 6 6, 3 2, 2
  12. 12. <ul><li>Pure strategy – Each participant selects one course of action </li></ul><ul><li>Mixed strategy requires randomly mixing different alternatives </li></ul><ul><li>Every finite game will have at least one equilibrium </li></ul>
  13. 13. <ul><li>Non cooperative games </li></ul><ul><li>Cooperative games </li></ul><ul><li>Repeated games </li></ul><ul><li>Sequential games </li></ul>
  14. 14. <ul><li>Not possible to negotiate with other participants </li></ul><ul><li>Because the two participants are interrogated separately, they have no idea whether the other person will confess or not </li></ul>
  15. 15. <ul><li>Possibility of negotiations between participants for a particular strategy </li></ul><ul><li>If prisoners jointly decide on not confessing, they would avoid spending any time in jail </li></ul><ul><li>Such games are a way to avoid prisoner’s dilemma </li></ul>
  16. 16. <ul><li>Yet another way to escape prisoner’s dilemma </li></ul><ul><li>If exercise is repeated multiple times, reactions become predictable </li></ul><ul><li>Acc. to eg in PD, both firms select high advertising & capture max. profit </li></ul><ul><li>But, if this exercise is repeated, outcomes may change </li></ul><ul><li>Advantage becomes temporary </li></ul><ul><li>Winning strategy- ‘tit for tat’ </li></ul>
  17. 17. <ul><li>Infinitely Repeated Game </li></ul><ul><ul><li>Co-operative behaviour is a rational response to a tit for tat strategy </li></ul></ul><ul><li>Finite Number of Repetitions </li></ul><ul><ul><li>Strategise to take action in the last period of time in order to have a long term effect </li></ul></ul>
  18. 18. <ul><li>One player acts first & then the other responds </li></ul><ul><li>2 firms contemplating the introduction of an identical product in the market </li></ul><ul><li>1 st firm- develop brand loyalties, associate product with the firm in minds of consumers </li></ul><ul><li>Thus, first mover advantage </li></ul>
  19. 19. <ul><li>Assume firms use maximum criterion, so neither should introduce a new product and earn $2 mn each </li></ul><ul><li>Firm 1 introduces a new product, firm 2 will still decide to stay out because right now it is losing $5 mn, opposed to $7 mn otherwise. </li></ul>Firm 2 No new product Introduce new product Firm 1 No new product $2, $2 $-5, $10 Introduce new product $10, $-5 $-7, $-7

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