Chapter 1. Chapter 16

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Prisoner’s dilemmas are common in real life, but not all real-life games are as dismal as the prisoner’s dilemma. One game, known as “stag hunt,” describes situations where cooperation is possible but fragile.The philosopher Jean-Jacques Rousseau described the game. He said that a lot of social situations are like going hunting with a friend: If you both agree to hunt for a stag, then you each have to hold your positions near each end of a valley so that the animal can’t escape. If you both hold to your positions, then you will almost surely get your kill. If one hunter wanders off to hunt the easier-to-find rabbit, however, then the stag will almost surely get away. Rabbit hunting works fine as a solo sport, but to catch a stag, you need a team effort.

This is the usual way of writing the game:

If Rousseau is quite sure that Hume will hunt stag, he will O7/XBgrfrVtoV7uyH9g88fKuW1rDXXvM+wNI7g==.

Correct! From the table, we can see that both Hunt Stag and Hunt Rabbit are likely outcomes, but Hunt Stag is riskier since Hunt Rabbit has a guaranteed payoff, implying a level of trust is required to achieve that outcome. If Rousseau is “quite sure” that Hume will play Hunt Stag, that should be a sufficient amount of trust to make that outcome feasible.

Sorry! Consider Rousseau’s best response in this situation if he is quite sure that Hume will hunt stag. To review how to determine the equilibrium of a game, please see the section “The “Best” Product May Not Always Win.”

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If Rousseau is quite sure that Hume will hunt rabbit, Rousseau will 7vMRmR/+kqb0EdZcn7p+vhl7Rcw/OTMwNYECrI6+hyc=.

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There are two Nash equilibria in this game. In the first one, Rousseau +yW1+qi1LhCQ8R68G1hx0RUV/gCcZsUwth1VXQ== while Hume +yW1+qi1LhCQ8R68G1hx0RUV/gCcZsUwth1VXQ==. In the second one, Rousseau qtK7Xr5jh9EU+TKcVx/dZhWunNuw3fhykE/RQQ== while Hume qtK7Xr5jh9EU+TKcVx/dZhWunNuw3fhykE/RQQ==.

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Of these two equilibria, economists call O4SDRDzDquefVvL5qHPyx3mFmrPZOfw577XEpeyDjpZoJhRdFXOa9znbFwEpT4vndPsz2C3+pL/xUR+NwFtIEgYDl3HkWe0Y9ZHjJUKjJE7j+4FA3pPNMMKhGCuuJPwvG3+JRkAd0GphbajkDPGtWw== the “payoff-dominant equilibrium” and WlMIq81KMZj0gDe4ggpQUsKdxfiKfHbkRU5ZpZp/OsnHQHAu/wpOuBJlNjuIMwrUFqU+Hm2O8svbLqvA/U/0TscW0EUzoY3QQGX9j7yxZjyaZfzTYdsHHZZhrzhx9EELebTs7P0hyG9lNzu/BVMf2g== the “risk-dominant equilibrium.” The G8Td6GDFjZuxVjLoEHbkQkdPQbfQMQbzgoZOxEpry5xhlzqk6jxCoD+XWx1L3pOEULIh73YgTUzLn+3AhjMx1bASp6fv26jJDy3jFYd/l+0UHx5t2aPrSrxDnilZ6HOGLtYj/vstXDCoAElDd15o5/gHIsyQ6XUrnedBjH7mo81lEjkrphIZz1+93nl3JjkEh2J6tFZhX2cIyF9k4+jDipYkR6Evi2Dy is the biggest risk that might push someone to choose the “risk-dominant equilibrium.”

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