Coordination Game - Examples

Examples

A typical case for a coordination game is choosing the sides of the road upon which to drive, a social standard which can save lives if it is widely adhered to. In a simplified example, assume that two drivers meet on a narrow dirt road. Both have to swerve in order to avoid a head-on collision. If both execute the same swerving maneuver they will manage to pass each other, but if they choose differing maneuvers they will collide. In the payoff matrix in Fig. 2, successful passing is represented by a payoff of 10, and a collision by a payoff of 0.

In this case there are two pure Nash equilibria: either both swerve to the left, or both swerve to the right. In this example, it doesn't matter which side both players pick, as long as they both pick the same. Both solutions are Pareto efficient. This is not true for all coordination games, as the pure coordination game in Fig. 3 shows. Pure (or common interest) coordination is the game where the players both prefer the same Nash equilibrium outcome, here both players prefer partying over both staying at home to watch TV. The {Party, Party} outcome Pareto dominates the {Home, Home} outcome, just as both Pareto dominate the other two outcomes, {Party, Home} and {Home, Party}.

This is different in another type of coordination game commonly called battle of the sexes (or conflicting interest coordination), as seen in Fig. 4. In this game both players prefer engaging in the same activity over going alone, but their preferences differ over which activity they should engage in. Player 1 prefers that they both party while player 2 prefers that they both stay at home.

Finally, the stag hunt game in Fig. 5 shows a situation in which both players (hunters) can benefit if they cooperate (hunting a stag). However, cooperation might fail, because each hunter has an alternative which is safer because it does not require cooperation to succeed (hunting a hare). This example of the potential conflict between safety and social cooperation is originally due to Jean-Jacques Rousseau.