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The Stag Hunt is a bimatrix game that appears similar to the prisoner's dilemma, but differs in that mutual cooperation is a Nash equilibrium, since the incentive to defect is removed by the reduced payoffs in the off-diagonal entries:

                                         Defect       Co-operate
                                    +--------------+--------------+
                                    |              |              |
                     Defect         |   1  , 1     |   2  ,  0    |
                                    |              |              |
                                    +--------------+--------------+
                                    |              |              |
                     Co-operate     |   0  , 2     |   3 ,  3     |
                                    |              |              |
                                    +--------------+--------------+

The game is so named as it describes the problem faced by two hunters who can independently choose whether to hunt a stag or a hare. A lone hunter will fail to catch a stag, and thus requires the cooperation of the other to do so; by playing it safe, a hunter can guarantee that they will catch a hare, but this is of less value to them.

The stag hunt may be a more appropriate model than the prisoner's dilemma in a given scenario (be it from biology, sociology or economics), and determining which is correct requires an accurate measure of the utility of each outcome to the participants. For instance, adding a guilt or punishment element to the Prisoner's dilemma may reduce it to a stag hunt, thus making mutual cooperation a rational choice (as is often observed experimentally).

The Stag hunt is also of theoretical interest, since it demonstrates a limitiation of Nash's theorem- whilst existence of a Nash equilibrium is ensured, it needn't be unique. Indeed, the Stag hunt has three Nash equilibria: mutual defection (a pure strategy of p=(1,0) by each player); mutual cooperation (a pure strategy of p=(0,1) by each player); and a mixed strategy p=(1/2,1/2). Thus knowledge of the existence of Nash Equilibria does not necessarily inform a choice of strategy; only confirm that players identifying themselves in equilibrium would be best served to remain so.


Part of A survey of game theory- see project homenode for details and links to the print version.

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