GAME THEORY SESSION 1 A BEAUTIFUL MIND • https://www.youtube.com/watch?v=2d_dtTZQyUM 2/15/23 GAME AND STRATEGIC DECISIONS • If I believe that my competitors are rational and act to maximize their own payoffs, how should I take their behavior into account when making my decisions? 2/15/23 NON COOPERATIVE VS. COOPERATIVE GAMES • In cooperative games, binding contracts are possible (Ex. Rugs, New technology); in noncooperative games, they are not (Ex. Food delivery, placements). 2/15/23 NON COOPERATIVE GAMES 2/15/23 It is essential to understand your opponent’s point of view and to deduce his or her likely responses to your actions. MARTIN SHUBIK- DOLLAR GAME RULES: 2/15/23 1. Bet for it. 2. The winner gets Rs. 100 when the college opens on 20th. 3. The runner up will not get anything but will have to pay the money he quoted. DOMINANT STRATEGIES • One that is optimal no matter what an opponent does. 2/15/23 WHAT SHOULD FIRMS A AND B DO? 2/15/23 EQUILIBRIUM IN DOMINANT STRATEGIES • Equilibrium in dominant strategies Outcome of a game in which each firm is doing the best it can regardless of what its competitors are doing. 2/15/23 WHAT SHOULD FIRMS A AND B DO? 2/15/23 NASH EQUILIBRIUM • All dominant strategies are Nash equilibria but not vice versa. • The Nash equilibrium does not necessarily correspond to the outcome that maximizes the aggregate profit of the players. 2/15/23 PRISONERS’ DILEMMA Two suspects in a crime, David and Ron, are arrested and placed in separate cells. The police, who have no real evidence against either, privately give each prisoner the chance to confess and implicate the other suspect for the crime. They tell each prisoner that if neither confesses, both will be convicted on a minor charge and will serve just 1 year in jail. If both confess, both will be convicted of the more serious crime but will be treated somewhat leniently because they cooperated, and each will go to jail for 5 years. But if one suspect confesses and the other doesn’t, the one that confesses will go free, while the other will be convicted of the crime and spend 10 years in jail. 2/15/23 PRISONERS’ DILEMMA 2/15/23 PRODUCT CHOICE PROBLEM 2/15/23 HOTELLING’S MODEL OF SPATIAL DISTIBUTION • BEACH LOCATION GAME 2/15/23 WHY DO SHOPS & VENDORS CLUSTER IN THE SAME AREA? • https://www.youtube.com/watch?v=jILgxeNBK_8 2/15/23 MAXIMIN VS. MAXIMAX STRATEGIES • Maximin: A maximin strategy is where a player chooses the best of the worst pay-off. Relevant when a player cannot rely on the other party to keep any agreement that has been made. • Maximax: A maximax strategy is one where the player attempts to earn the maximum possible benefit available. Also called best of best strategy. 2/15/23 CONTD. In the case of dominant strategy, both the optimistic maximax and pessimistic maximin lead to the same decision being taken. 2/15/23 DOMINATED STRATEGY It is the opposite of a dominant strategy. A strategy is dominated when the player has another strategy that gives it a higher payoff no matter what the other player does. 2/15/23 HOW TO FIND NASH EQUILIBRIA? 2/15/23 HOW TO FIND NASH EQUILIBRIA? 2/15/23 SUMMARY • Finding a Nash Equilibrium by Identifying Dominant Strategies and Eliminating Dominated Strategies 1. Whenever both players have a dominant strategy, those strategies will constitute the Nash equilibrium in the game. 2. If just one player has a dominant strategy, that strategy will be the player’s Nash equilibrium strategy. We can find the other player’s Nash equilibrium strategy by identifying that player’s best response to the first player’s dominant strategy. 3. If neither player has a dominant strategy, but both have dominated strategies, we can often deduce the Nash equilibrium by eliminating the dominated strategies and thereby simplifying the analysis of the game. 2/15/23
