Games People Play. 9: Collective-Action Games In collective-action games the interests of society and the individuals are in conflict

Games People Play. Collective-Action Games Come in three familiar forms Prisoners dilemma games Chicken games Assurance games Typically they involve many players, although we shall simplify them to the case of two for clarity.

Games People Play. Collective-Action Games The Prisoners dilemma as a collective-action game Consider the standard public goods problem. Two farmers share a supply of water from the mountains. Each can work on maintaining the canal that supplies them both with water, or they can work on their own crops. This leads to payoffs of the following form. Farmer #2 CanalLand Farmer#1Canal 4,4 -1,6 Land 6,-1 0,0

Games People Play. The prisoners dilemma as a collective-action game Farmer #2 CanalLand Farmer#1 Canal 4,4 -1,6 Land 6,-1 0,0 This is the standard prisoners dilemma. Each farmer tends his own land and we get the socially sub-optimal Nash equilibrium {0,0}. Not the socially optimal {4,4}. Not the socially optimal {4,4}.

Games People Play. The prisoners dilemma as a collective-action game II Farmer #2 CanalLand Farmer#1 Canal 2.3,2.3 -1,6 Land 6,-1 0,0 Again we see that there is a divergence between the socially optimal {-1,6} or {6,-1} and the Nash {0,0}. Here there is a particularly difficult problem to solve as both farmers prefer to be the one receiving 6.

Games People Play. Chicken as a collective action game Farmer #2 CanalLand Farmer#1 Canal 5,5 2,6 Land 6,2 0,0 Now our trusty yeomen must coordinate to avoid the pitfalls of the chicken game.

Games People Play. Collective-Action Games The Stag Hunt (An assurance game) The French philosopher, Jean Jacques Rousseau, presented the following situation. Two hunters can either jointly hunt a stag (an adult deer and rather large meal) or individually hunt a rabbit (tasty, but substantially less filling). Hunting stags is quite challenging and requires mutual cooperation. If either hunts a stag alone, the chance of success is minimal. Hunting stags is most beneficial for society but requires a lot of trust among its members. Hunter #2 StagRabbit Hunter#1 Stag 10,10 0,8 Rabbit 8,0 7,7

Games People Play. Collective-Action Games The Stag Hunt There are two pure strategy equilibria. Both players prefer one equilibrium to the other. However, the inefficient equilibrium is less risky as the payoff variance over the other player's strategies is lower. Specifically, one equilibrium is payoff- dominant while the other is risk-dominant. Hunter #2 StagRabbit Hunter#1 Stag 10,10 0,8 Rabbit 8,0 7,7

Games People Play. Collective-Action Games A Possible Solution – Correlated Equilibria Consider the following version of the Chicken Game Farmer #2 CanalLand Farmer#1 Canal 5,5 2,10 Land 10,2 0,0

Games People Play. Collective-Action Games Correlated Equilibria Each farmer prefers a different equilibrium, making sure that they are coordinated on the same one is good for society. Suppose that each could give their strategy choice to a trusted third party. The trusted third party tells them that they will allocate a role to one farmer according to some random mechanism Farmer one is told that a coin will be flipper and if it comes out heads he gets to play “Land” otherwise he must play “Canal”. Both farmers observe the coin toss. Each farmer gets an expected value of 6 from this. Deviating from the allocated role hurts either farmer and will not occur. This is a correlated equilibrium.