# If the market as a game is played just once allow for

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If the market-as-a-game is played just once allow for a unique payoff of (2, 2). It can be any number but both players receive exactly the same amount. Each player knows exactly what they want to do (they have a dominant strategy) and each player has the easiest of decisions to face – keep prices high and receive 2. Both players would prefer to be in the top left cell of the matrix because in four cycles of this game a player could receive a payoff of 8 = 2+2+2+2. However, player A has a dominant strategy of competing to a low price, trying to do better by obtaining a payoff of 3. But the 3 is only obtainable if player B continues to keep his prices high. Signalling, Strategy & Management Type 75
Table 8.1 Prisoners’ Dilemma In other words, if B keeps prices high, it is because he trusts A to do likewise and vice vearsa . So B trusts A; but A knowing that, betrays B. Once player B realises that player A has lowered its price, player B follows and they both 12 find themselves in the lower right cell of the matrix with a payoff of (1,1). Player A now ends up with 6 = 2+3+1+0 or with 4 = 1+1+1+1 if B punishes A for the betrayal by always keeping prices low. This is a recognised punishment strategy , signalling to A the payoff 4 in time period t+1 instead of 8. In trying to do better you can end up worse off! David Hume, an English philosopher, writing in the 18 th century, captured the idea: ‘we can better satisfy our appetites in an oblique manner, than by their headlong and impetuous motion’. Remember that the future is not what it used to be! Nash equilibrium In the exchange of prices, players interact with each other by using prices as signals. An incumbent and entrant, or two incumbents can face classic coordination problems. Conflicts can arise. In a two-person game, a pair of strategies will form a Nash equilibrium when each player cannot do better given the strategy the other player has adopted. A Nash equilibrium is a pair of strategies such that each is a best response to the other. The payoff (1,1) above is an example of a Nash equilibrium. To test whether a strategy combination forms a Nash equilibrium just consider the following: let us call the strategy for the first player x* and the strategy for the second player y*. A pure strategy equilibrium is a Nash equilibrium in which the equilibrium strategies are played with certainty or with probability equal to one. When the Nash equilibrium involves only strategies that are played with certainty, we have a pure strategy Signalling, Strategy & Management Type 76 High p Player B Low p Player A High p 2, 2 3, 0 Low p 0, 3 1, 1 12 A cartel between A and B might seem a solution, but with an inherent incentive to cheat or betray, enforcement of the cooperative solution might prove to be difficult, vide the arguments in McNutt Law, Economics and Antitrust . Cartels may not last very long. If one player believes that the other player will always cooperate and keep prices high then there is an incentive to betray or cheat. The