Coordination game
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.
[1] An assurance game is commonly referred to as a “stag hunt” (Fig.5), which represents the following scenario.
Thus, the scenario where both hunters choose to coordinate will provide the most beneficial output for society.
A common problem associated with the stag hunt is the amount of trust required to achieve this output.
5 shows a situation in which both players (hunters) can benefit if they cooperate (hunting a stag).
This example of the potential conflict between safety and social cooperation is originally due to Jean-Jacques Rousseau.
[4] Since the couple want to spend time together, they will derive no utility by doing an activity separately.
Unlike the other forms of coordination games described previously, knowing your opponent’s strategy won’t help you decide on your course of action.
The pure Nash equilibria are the points in the bottom left and top right corners of the strategy space, while the mixed Nash equilibrium lies in the middle, at the intersection of the dashed lines.
Unlike the pure Nash equilibria, the mixed equilibrium is not an evolutionarily stable strategy (ESS).
The mixed Nash equilibrium is also Pareto dominated by the two pure Nash equilibria (since the players will fail to coordinate with non-zero probability), a quandary that led Robert Aumann to propose the refinement of a correlated equilibrium.
Often we are confronted with circumstances where we must solve coordination problems without the ability to communicate with our partner.
For instance, some equilibria may give higher payoffs, be naturally more salient, may be more fair, or may be safer.
One such experiment by Bortolotti, Devetag, and Andreas Ortmann was a weak-link experiment in which groups of individuals were asked to count and sort coins in an effort to measure the difference between individual and group incentives.
Conversely, game theorists have modeled behavior under negative externalities where choosing the same action creates a cost rather than a benefit.
While 101 is shorter, 280 is considered more scenic, so drivers might have different preferences between the two independent of the traffic flow.
But each additional car on either route will slightly increase the drive time on that route, so additional traffic creates negative network externalities, and even scenery-minded drivers might opt to take 101 if 280 becomes too crowded.
A well-known example of the minority game is the El Farol Bar problem proposed by W. Brian Arthur.
