# Both firms have a dominant strategy which is to

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Both firms have a dominant strategy which is to choose a low price, so the likely outcome of thegame is for both firms to choose a low price and they each make a profit of 100. If they couldsomehow agree to each choose a high price, they could each make a profit of 500 which isclearly better for both firms. The problem is that each firm has an incentive to cheat on such anagreement. They cannot make a legally binding contract because such a contract is illegal in theUnited States.This is where the guaranteed price matching scheme comes in. If firm A, for example, were toannounce that if firm B chooses a low price then firm A will match it, then firm B no longer hasan incentive to choose a low price! The guaranteed price matching scheme is actually a way forthe firms to keep the price in the market high, which is good for the firms but not good for theconsumers!!Note that it is not always the case that each player has a dominant strategy. Yet often it may bepossible in such a situation for a game to have a predictable outcome. Suppose, for example, thatin another situation firm C does not have a dominant strategy, but firm D does (and firm Crecognizes that dominant strategy). Then firm C will choose its strategy based on its expectationof what firm D will do. This describes what is called aNash equilibriumin game theory –acombination of strategies where no player can improve their payoff by changing strategies,given the strategies chosen by the other players.
Nash Equilibrium: A combination of strategies where no player can improve theirpayoff by switching to another of their strategies, given the strategy or strategieschosen by the other player(s).There are two additional aspects of game theory that we consider briefly here: maximin strategyand sequential games. Amaximin strategyin game theory is a strategy designed tomaximizethe minimum gain that can be earned. Such a strategy may be desirable when a playerconfronts considerable uncertainty and a risk of a large potential loss. Consider the followingpayoff matrix where Player A can choose either the Top row or the Bottom row. Player Bchooses either the Left column or the Right column. For each strategy combination, the numberon the left is the payoff to Player A, and the number on the Right is the payoff to player B. Sofor example, if Player A plays Top and Player B plays Left, then Player A gets 2 and Player Bgets 5.

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