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Concept
Coordination game
Summary
A coordination game is a type of simultaneous game found in game theory. It describes the situation where a player will earn a higher payoff when they select the same course of action as another player. The game is not one of pure conflict, which results in multiple pure strategy Nash equilibria in which players choose matching strategies. Figure 1 shows a 2-player example.
{| class="wikitable" style="background:white;color:maroon;text-align:center;float:right;"
| style="background:white; border:1px solid white;" colspan="2" rowspan="2"| || style="background:White; color:black; border:1px solid white; font-weight:bold;" align="center" colspan="2"| Player 2
| style="color:cadetblue;"|Left||style="color:cadetblue;"|Right
| style="background:white; color:black; border:1px solid white; font-weight:bold;" valign="center" rowspan="2"|Player 1 || style="color:cadetblue;" align="left"|Up || 2,4 || 1,3
| style="color:cadetblue;" align="left"|Down || 1,3 || 2,4
| style="background:white; border:1px solid white;" colspan="4"|
| style="background:white; border:1px solid white;" colspan="4"|
| style="background:white; border:1px solid white;" align="left" colspan="4"| Figure 1: Payoffs for a Coordination Game (Player 1, Player 2)
|}
Both (Up, Left) and (Down, Right) are Nash equilibria. If the players expect (Up, Left) to be played, then player 1 thinks their payoff would fall from 2 to 1 if they deviated to Down, and player 2 thinks their payoff would fall from 4 to 3 if they chose Right. If the players expect (Down, Right), player 1 thinks their payoff would fall from 2 to 1 if they deviated to Up, and player 2 thinks their payoff would fall from 4 to 3 if they chose Left. A player's optimal move depends on what they expect the other player to do, and they both do better if they coordinate than if they played an off-equilibrium combination of actions. This setup can be extended to more than two strategies or two players.
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.
Official source
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