Coordination game
From Free net encyclopedia
The coordination game is a classic (symmetric) two player, two strategy game, with payoff matrix as follows:
| Player 2 adopts strategy 1 | Player 2 adopts strategy 2 | |
| Player 1 adopts strategy 1 | A | B |
| Player 1 adopts strategy 2 | C | D |
where A>C and D>B. Rational players will thus cooperate on either of the two strategies to receive a high payoff. Players in the game must agree on one of the two strategies in order to receive a high payoff. If the players do not agree, they receive a lower payoff.
Contents |
Examples
Consider a new product where two technologies are available to two firms with compatible products, and they have to elect a strategy to become the market standard. If both firms agree on the chosen technology, high sales are expected for both firms. If the firms do not agree on the standard technology, few sales result. Both strategies are Nash equilibria of the game.
Driving on a road, and having to choose either to drive on the left or to drive on the right of the road, is also a coordination game. For example, with payoffs 100 meaning no crash and 0 meaning a crash, the coordination game can be defined with the following payoff matrix:
| Drive on the Left: | Drive on the Right: | |
| Drive on the Left: | 100 | 0 |
| Drive on the Right: | 0 | 100 |
In this case there are two pure strategy Nash equilibria:
- both choose to either drive on the left
- both on the right.
If we admit mixed-strategies (where a pure strategy is chosen at random, subject to some fixed probability), then there are three Nash equilibria for the same case: two we have seen from the pure-strategy form, where the probabilities are (0%,100%) for player one, (0%, 100%) for player two; and (100%, 0%) for player one, (100%, 0%) for player two respectively. We add another where the probabilities for each player are (50%, 50%). (This final case simply says that if everyone else drives on a random side of the road you won't do any better than picking a random side yourself, however, all proportions yield indifferently bad payoffs in this case.)
Coordination and equilibrium selection
Games like the driving example above have illustrated the need for solution to coordination problems. Often we are confronted with circumstances where we must solve coordination problems without the ability to communicate with our partner. Many authors have suggested that particular equilibria are focal for one reason or another. For instance, some equilibria may give higher payoffs, be naturally more salient, may be more fair, or may be safer. Sometimes these refinements conflict which lead to some of the other interesting coordination games (e.g. Stag hunt and Battle of the sexes).
Other coordination games
References
Lewis, David (1969) Convention: A Philosophical Study. Oxford: Blackwell.