Oligopoly & Game Theory Lecture 26 Dr. Jennifer P. Wissink ©2016 John M. Abowd and Jennifer P. Wissink, all rights reserved. May 4, 2016

Announcements 1110(micro) Spring 2016 u Important end-of-semester reminders –Register for early-makeup final on Bb if you plan to sit the final then – see policy there. –Check Bb under Tools: i>clicker registration & points and make sure your device is registered with your name for this class! u Check MEL frequently to make sure you reach your magic number of 500 MEL points. –To see your current number of MEL points, logon to MEL, Click Results, –Then Click Show Overall Score, –Then look at Completed Assignments Weighted points earned u Check Bb Announcement Page. Open the page and make sure you check out anything that is there. –Especially i>clicker add-on info & any office hours additions/changes

Monopolistic Competition: Performance (Efficiency & Equity) u i>clicker question Is the monopolistically competitive firm Pareto/Allocatively Efficient? A. Yes. B. No. C. Maybe so u i>clicker question Is the monopolistically competitive firm productively efficient? A. Yes. B. No. C. Maybe so q GV P GV lrmc demand for GV jeans mr GV $ q

Up Next: Oligopoly

Oligopoly: Structure Competition Among A Few u In an oligopoly there are very few sellers of the good. u The product may be differentiated among the sellers (e.g. automobiles) or homogeneous (e.g. gasoline). u Entry is often limited either by legal restrictions (e.g. banking in most of the world) or by a very large minimum efficient scale (e.g. overnight mail service) or by strategic behavior. u Sill assuming complete and full information.

Oligopoly: Conduct u Harder to model! (Compared to perfect competition and monopoly and monopolistic competition) u In an oligopoly –firms know that there are only a few large competitors –competitors take account of the effects of their actions on the market u To predict the outcome of such a market, economists frequently use game theory methods.

Game Theory: Setup u List of players: all the players are specified in advance. u List of actions: all the actions each player can take are spelled out. u Rules of play: who moves and when is spelled out. u Information structure: who knows what and when is spelled out. u Strategies: the set of actions players can use. u Payoffs: the amount each player gets for every possible combination of the players’ strategies. u Solution or equilibrium concept: a way you reason that players select strategies to play, and then consequently how you predict the outcome of the game.

Dominant Strategy Equilibrium u A Dominant Strategy for player “i” is a strategy such that player’s i’s payoff from playing that strategy is at least as large as the payoff player i would get from playing any other strategy, no matter what player i’s rivals choose as their strategies. u A Dominant Strategy Equilibrium of a game occurs when each player of the game has and plays his/her dominant strategy. u Lots of interesting games have dominant strategy equilibriums. u And for lots of interesting and fun games DON’T.

The Prisoners’ Dilemma Game & Dominant Strategy Equilibrium u Roger and Chris have been accused of a major crime (which they committed). –They also have outstanding warrants based on minor crimes, too. u They are held in isolated cells and offered the choice to either Lie or Confess. u The payoff matrix shows the number of years of prison Roger (the row player) and Chris (the column player) will receive depending upon who confesses and who lies as (Roger’s prison time, Chris’ prison time). u The game is played one-shot, simultaneously and non-cooperatively with full information.

The Prisoners’ Dilemma: Solution u Roger’s best response (shown in yellow): –If Chris lies, then Roger should confess (Roger gets 0 years of jail, which is better than 1 year in jail). –If Chris confesses, then Roger should confess (Roger gets 5 years of jail, which is better than 6 years in the slammer). u Chris’s best response (shown in green): –If Roger lies, then Chris should confess (Chris gets 0 years of jail). –If Roger confesses, then Chris should confess (Chris gets 5 years of jail).

The Prisoners’ Dilemma: Solution u There is a single dominant strategy equilibrium: –Roger confesses and Chris confesses. –They both go to jail for 5 years. u The table shows that the dominant strategy is also the Nash equilibrium for this game. u Only the payoff (-5,-5) has both a yellow and a green highlight—indicating that it is the best response for both players, given what the other is doing.

The Prisoners’ Dilemma Is Very Distressing..., Or Is It? u In the Prisoners’ Dilemma game, the “superior” outcome is when both prisoners lie – but that requires cooperation. u When the game is only played once, simultaneously and non-cooperatively, (confess, confess) is the dominant strategy equilibrium and (-5, -5) is the dominant strategy equilibrium outcome. u Could Roger & Chris sustain the (lie, lie) outcome of (-1, -1) somehow? –change the payoffs in the matrix –play the game repeatedly u Do all games have at least one dominant strategy equilibrium? –NO! –Then what?

Nash Equilibrium u Named after John Nash - a Nobel Prize winner in Economics. –Did you read or see A Beautiful Mind? u A Nash Non-cooperative Strategy (Best Response) for player “i” is a strategy such that player’s i’s payoff from playing that strategy is at least as large as the payoff player i would get from playing any other strategy, given the strategies the others are playing. u A Nash Non-cooperative Equilibrium is a set of (Nash) strategies for all players, such that, when played simultaneously, they have the property that no player can improve his payoff by playing a different strategy, given the strategies the others are playing.

Hotelling's Location Game (Nash Equilibrium in Location)

The Price Game Chris Roger LowHigh Low 20, 2060, 0 High0, 60100, 100