EC102: Class 9 Christina Ammon

Game Theory - Concepts Players Actions Strategies Pay-offs Nodes What do we assume about the information set? An equilibrium is described in terms of strategies not in terms of pay-offs

Simultaneous Games In simultaneous games no one can observe the actual strategy played by the other - less information than in a sequential game

Question 1 Beta’s dominant strategy is: If Air Lion produces “high”, then Beta produces “high”, and if Air Lion produces “low”, then Beta produces “low” Beta produces “low” no matter what Air Lion does Beta produces “high” no matter what Air Lion does If Air Lion produces “high”, then Beta produces “low”, and if Air Lion produces “low”, then Beta produces “high”

Question 1 What is a dominant strategy? A dominant strategy is a strategy that is optimal independent of the other player’s actions. What is a dominant strategy equilibrium ? A dominant strategy equilibrium is where both players have a dominant strategy.

Question 1 Beta’s dominant strategy is: If Air Lion produces “high”, then Beta produces “high”, and if Air Lion produces “low”, then Beta produces “low” Beta produces “low” no matter what Air Lion does Beta produces “high” no matter what Air Lion does If Air Lion produces “high”, then Beta produces “low”, and if Air Lion produces “low”, then Beta produces “high”

Nash equilibrium vs. Perfect Equilibrium Simultaneous games – just need the Nash condition Nash condition: Strategies are chosen such that no player has an incentive to deviate given the other player’s strategy => A Nash equilibrium is an equilibrium which satisfies the Nash condition Credibility condition: Strategies are such that no player has an incentive to deviate at any given node. =>A (Subgame) Perfect Equilibrium is an equilibrium that satisfies both the Nash and the Credibility Condition

Question 2 Which of the following pairs of strategies satisfies the Nash condition? General plays “stay out”; Liege plays “high output” no matter what General does General plays “enter”; Liege plays “low ouput” if General play “enter” and “high output” if General plays “stay out” Both of the above pairs of strategies

Finding the equilibrium in sequential games Finding the Perfect Equilibrium: backward induction I.e. work backwards in time Start in the last time period and find the optimal strategy at each node Take as given that in last period will play optimal strategies Given these optimal strategies, what is optimal in the period before Work backwards until period 0 Finding (all) Nash Equilibria: usually not required, just know how to check

Question 3 Which of the following pairs of strategies satisfies the Credibility condition? General plays “stay out”; Liege plays “high output” no matter what General does General plays “enter”; Liege plays “low ouput” if General play “enter” and “high output” if General plays “stay out” Both of the above pairs of strategies

Question 4 Which of the following statements is correct? Strategic investment effects arise under perfect competition Strategic investment effects arise under monopolistic competition Strategic investment effects arise under monopoly with blocked entry All three previous statements are wrong

Question 4 What are strategic investments? What are the requirements for anyone wanting to undertake these investments? Non-zero profits Entry has to be possible (though not free, as otherwise zero profits) In which market scenario are these satisfied?

Question 4 Which of the following statements is correct? Strategic investment effects arise under perfect competition Strategic investment effects arise under monopolistic competition Strategic investment effects arise under monopoly with blocked entry All three previous statements are wrong

Question 5 Consider a penalty shoot-out with three choices for the kicker and the goalie: right, left or middle. An outcome in which each player goes right 40 per cent of the times is: An equilibrium in pure strategies An equilibrium in mixed strategies Not an equilibrium in either strategies

Question 5 What is a mixed strategy equilibrium? Any pure strategy equilibrium is in principle a mixed strategy equilibrium – with probability 1 assigned to one strategy, but we solve for it differently There always exists an equilibrium in mixed strategies How do we test if a set of strategies are an equilibrium Look if someone has an incentive to deviate, or Check if given the probability chosen by the other player makes the first player indifferent between all actions in expectation Finding a mixed strategy equilibrium: Finding the probability for each player that will make the other player indifferent between all actions This has to be consistent across both players

Question 5

Question 5 Consider a penalty shoot-out with three choices for the kicker and the goalie: right, left or middle. An outcome in which each player goes right 40 per cent of the times is: An equilibrium in pure strategies An equilibrium in mixed strategies Not an equilibrium in either strategies

Question 6 “I recognized that information was, in many respects, like a public good, and it was this insight that made it clear to me that it was unlikely that the private market would provide efficient resource allocations whenever information was endogenous.” (Joseph Stiglitz)

Question 6 What is a public good? Non-rival Non-excludable “The defining characteristic of a public good is that consumption of it by one individual does not actually or potentially reduce the amount available to be consumed by another individual” (Gravelle and Rees).  Why is a public good not efficiently allocated? In how far is information like a public good? Is it non-rival? Is it non-excludable?