games people play. 9: collective-action games in collective-action games the interests of society...

Games People Play.Games People Play.

9: Collective-Action Games9: Collective-Action Games

In collective-action games the interests of In collective-action games the interests of society and the individuals are in conflictsociety and the individuals are in conflict


Collective-Action GamesCollective-Action Games

Come in three familiar formsCome in three familiar formsPrisoners dilemma games

Chicken games

Assurance games

Typically they involve many players, although we shall simplify them to the case of two for clarity.



The Prisoners dilemma as a collective-action gameThe Prisoners dilemma as a collective-action game

Consider the standard public goods problem. Two farmers share a Consider the standard public goods problem. Two farmers share a supply of water from the mountains. Each can work on maintaining the 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 canal that supplies them both with water, or they can work on their own crops. This leads to payoffs of the following form.crops. This leads to payoffs of the following form.

Farmer #2Farmer #2

CanalCanal LandLand

FarmerFarmer

#1#1

CanalCanal 4,4,44 -1,-1,66

LandLand 6,6,-1-1 0,0,00


The prisoners dilemma as a The prisoners dilemma as a collective-action gamecollective-action game

Farmer #2Farmer #2

CanalCanal LandLand

FarmerFarmer

#1#1

CanalCanal 4,4,44 -1,-1,66

LandLand 6,6,-1-1 0,0,00

This is the standard prisoners dilemma. This is the standard prisoners dilemma.

Each farmer tends his own land and we get the socially sub-optimal Nash Each farmer tends his own land and we get the socially sub-optimal Nash equilibrium {equilibrium {0,0,0}.0}.

Not the socially optimal {Not the socially optimal {4,4,4}.4}.


The prisoners dilemma as a The prisoners dilemma as a collective-action game IIcollective-action game II

Farmer #2Farmer #2

CanalCanal LandLand

FarmerFarmer

#1#1

CanalCanal 2.3,2.3,2.32.3 -1,-1,66

LandLand 6,6,-1-1 0,0,00

Again we see that there is a divergence between the socially optimalAgain we see that there is a divergence between the socially optimal {{-1,-1,6} or {6} or {6,6,-1} and the Nash {-1} and the Nash {0,0,0}. 0}.

Here there is a particularly difficult problem to solve as both farmers Here there is a particularly difficult problem to solve as both farmers prefer to be the one receiving 6.prefer to be the one receiving 6.


Chicken as a collective action Chicken as a collective action gamegame

Farmer #2Farmer #2

CanalCanal LandLand

FarmerFarmer

#1#1

CanalCanal 5,5,55 2,2,66

LandLand 6,6,22 0,0,00

Now our trusty yeomen must coordinate to avoid the pitfalls of the Now our trusty yeomen must coordinate to avoid the pitfalls of the chicken game.chicken game.



The Stag Hunt (An assurance game)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 #2Hunter #2

StagStag RabbitRabbit

HunterHunter

#1#1

StagStag 10,10,1010 0,0,88

RabbitRabbit 8,8,00 7,7,77



The Stag HuntThe Stag HuntThere 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 #2Hunter #2

StagStag RabbitRabbit

HunterHunter

#1#1

StagStag 10,10,1010 0,0,88

RabbitRabbit 8,8,00 7,7,77



A Possible Solution – Correlated EquilibriaA Possible Solution – Correlated EquilibriaConsider the following version of the Chicken Game

Farmer #2Farmer #2

CanalCanal LandLand

FarmerFarmer

#1#1

CanalCanal 5,5,55 2,2,1010

LandLand 10,10,22 0,0,00



Correlated EquilibriaCorrelated EquilibriaEach 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.

games people play. 9: collective-action games in collective-action games the interests of society...

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