Strategic Decisions in Noncooperative Games Introduction to Game Theory

Definitions Game: Situation in which players (participants) make strategic decisions that take into account the actions and reactions of the other players. Cooperative Game: A game in which players can make binding commitments. Non-cooperative Game A game in which binding commitments are not possible. Payoff: Value of an outcome to a player. Strategy Rule or plan of action for playing a game; one player’s best response to each action taken by other players.

Goals, Strategies, Rules Each player chooses a strategy in order to maximize its payoff, given the actions of the other players. Optimal strategy A strategy that maximizes a player’s expected payoff. Dominant strategy A strategy that is optimal no matter what an opponent does. Dominant strategy equilibrium Outcome of a game in which each player is playing a dominant strategy. Simultaneous choice games Each player chooses its strategy at the same time, OR without knowing the other player’s choice

Advertising Game #1: Dominant Strategy Equilibrium Firm B AdvertiseDon’t Advertise Firm AAdvertise 10, 515, 0 Don’t Advertise 6, 810, 2

Advertising Game #2: No Dominant Strategy Equilibrium Firm B AdvertiseDon’t Advertise Firm AAdvertise 10, 515, 0 Don’t Advertise 6, 820, 2

A More General Equilibrium Concept Nash Equilibrium Each player plays its best response, given the actions of other players. No player can improve its payoff by changing its action. All dominant strategy equilibria are Nash equilibria. A Nash equilibrium is not necessarily a dominant strategy equilibrium A game may have One Nash equilibrium More than one Nash equilibrium Zero Nash equilibria

Product Choice: Commitments, Signals, and Nash Equilibrium Firm 2 CrispySweet Firm 1Crispy -5, -510, 10 Sweet 10, 10-5, -5

Is Product Choice a Prisoners’ Dilemma? Pepsi Introduce Energy Drink No Energy Drink CokeIntroduce Energy Drink 10, 1020, 5 No Energy Drink 5, 2015, 15

Beach Location Game Two competitors sell snacks and drinks at a beach that is 200 yards long with customers spread uniformly along this length. Customers always buy from the closest snack stand. Where on the beach will the snack stands locate in order to maximize sales? Compare to Gas station locations Locations of used car dealers Presidential elections