as well. The group of players, then, all plays This indifference point is Majority Majority. important, however, in determining which pure strategy will be an ESS since coordination games are, by definition, about trying to copy the choices other players make. Whichever strategy has the higher payoff at the outset of the game is the ESS for that group (Weibull 1995: 110). In the context of our model, if playing yields the greatest utility at the outset, this is the stable Majority ESS. Any player who unilaterally attempts to play will receive lower utility from doing Minority so, and will therefore return immediately to the higher-payoff strategy. This is true, of Majority course, even when would pay more if players were playing it. Minority all Once an ESS of exists, changes in players’ strategies are very difficult, even Majority when changes in increase the value of working with other members of the minority. Put w another way, once women are playing a strategy reflecting false tokenism behavior (i.e., it is quite difficult for them to play a strategy consistent with critical mass Majority, Majority), behavior (i.e., To see how this works, consider again the normal form game Minority, Minority). in Table 5.1. Suppose the value of is much greater than the value of Under these bw 1-w. circumstances, minority group members would derive much more utility for playing Minority than for playing Yet if one player unilaterally chooses she receives a payoff Majority. Majority, not of but of zero (0). Observing this lower payoff, she rationally returns to playing bw, thus preventing minority group members from enjoying the benefits of critical mass, Majority, regardless of how large those benefits become. This depiction makes clear that the critical mass problem is not one of numbers, as much of the previous literature has presumed, but rather of Increases in serve only to increase potential payoffs that minority group coordination. w members will never enjoy because they cannot overcome this coordination problem. In other words, minority group members began playing the game when playing was rational Majority
Majority as well. The group of players, then, all plays Majority. This indifference point is important, however, in determining which pure strategy will be an ESS since coordination games are, by definition, about trying to copy the choices other players make. Whichever strategy has the higher payoff at the outset of the game is the ESS for that group (Weibull 1995: 110). In the context of our model, if playing Majority yields the greatest utility at the outset, this is the stable ESS. Any player who unilaterally attempts to play Minority will receive lower utility from doing so, and will therefore return immediately to the higher-payoff Majority strategy. This is true, of course, even when Minority would pay more if all players were playing it. Once an ESS of Majority exists, changes in players’ strategies are very difficult, even when changes in w increase the value of working with other members of the minority. Put another way, once women are playing a strategy reflecting false tokenism behavior (i.e., Majority, Majority), it is quite difficult for them to play a strategy consistent with critical mass behavior (i.e., Minority, Minority). To see how this works, consider again the normal form game in Table 5.1. Suppose the value of bw is much greater than the value of 1-w. Under these circumstances, minority group members would derive much more utility for playing Minority than for playing Majority. Yet if one player unilaterally chooses Majority, she receives a payoff not of bw, but of zero (0). Observing this lower payoff, she rationally returns to playing Majority, thus preventing minority group members from enjoying the benefits of critical mass, regardless of how large those benefits become. This depiction makes clear that the critical mass problem is not one of numbers, as much of the previous literature has presumed, but rather of coordination. Increases in w serve only to increase potential payoffs that minority group members will never enjoy because they cannot overcome this coordination problem. In other words, minority group members began playing the game when playing Majority was rational
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