Editing Coordination game (section)

== 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|payoff matrix]] in Fig. 2, successful passing is represented by a payoff of 8, 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 efficiency|Pareto efficient]]. This game is called a ''[[pure coordination game]]''. This is not true for all coordination games, as the ''[[assurance game]]'' in Fig. 3 shows. 

An assurance game describes the situation where neither player can offer a sufficient amount if they contribute alone, thus player 1 should defect from playing if player 2 defects. However, if Player 2 opts to contribute then player 1 should contribute also.<ref>{{Cite web|title=Assurance Game - P2P Foundation|url=https://wiki.p2pfoundation.net/Assurance_Game#:~:text=Definition,to%20Cooperate%20as%20well.%22|access-date=2021-04-23|website=wiki.p2pfoundation.net}}</ref> An assurance game is commonly referred to as a “[[stag hunt]]” (Fig.5), which represents the following scenario. Two hunters can choose to either hunt a stag together (which provides the most economically efficient outcome) or they can individually hunt a Rabbit. Hunting Stags is challenging and requires cooperation. If the two hunters do not cooperate the chances of success is minimal. 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.<ref>{{Cite web|title=Assurance game - Game Theory .net|url=https://www.gametheory.net/dictionary/Games/AssuranceGame.html|access-date=2021-04-23|website=www.gametheory.net}}</ref> Fig. 5 shows a situation in which both players (hunters) can benefit if they cooperate (hunting a stag). As you can see, 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]].<ref>{{Cite web|title=Definition of Coordination Game {{!}} Higher Rock Education|url=https://www.higherrockeducation.org/glossary-of-terms/coordination-game|access-date=2021-04-23|website=www.higherrockeducation.org}}</ref>

{| style="margin:auto;"
|-
| [[File:Pure Coordination.png|center|frame|Fig. 2 ''Pure Coordination'']]
| [[File:Contribute, Defect.png|center|frame|Fig.3 ''Assurance Game'']]
|-
| [[File:Battle of the Sexes.png|center|frame|Fig. 4 ''Battle of the Sexes'']]
| [[File:Stag Hunt.png|center|frame|Fig. 5 ''Stag Hunt'']]
|}

This is different in another type of coordination game commonly called [[Battle of the sexes (game theory)|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. Assume that a couple argues over what to do on the weekend. Both know that they will increase their utility by spending the weekend together, however the man prefers to watch a football game and the woman prefers to go shopping.<ref>{{Cite web|title=Game theory II: Battle of the sexes {{!}} Policonomics|url=https://policonomics.com/lp-game-theory2-battle-of-the-sexes/|access-date=2021-04-26|language=en-US}}</ref>

Since the couple want to spend time together, they will derive no utility by doing an activity separately. If they go shopping, or to football game one person will derive some utility by being with the other person, but won’t derive utility from the activity itself. Unlike the other forms of coordination games described previously, knowing your opponent’s strategy won’t help you decide on your course of action. Due to this there is a possibility that an equilibrium will not be reached.<ref>{{Cite web|title=Game theory II: Battle of the sexes {{!}} Policonomics|url=https://policonomics.com/lp-game-theory2-battle-of-the-sexes/|access-date=2021-04-23|language=en-US}}</ref> 

=== Voluntary standards ===

In [[social sciences]], a voluntary standard (when characterized also as [[De facto standard|''de facto'' standard]]) is a typical solution to a coordination problem.<ref name="Ulmann">{{cite book|author=Edna Ullmann-Margalit|title=The Emergence of Norms|url=https://archive.org/details/emergenceofnorms0024ullm|date=1977|publisher=Oxford University Press|isbn=978-0-19-824411-0|url-access=registration}}</ref> The choice of a voluntary standard tends to be stable in situations in which all parties can realize mutual gains, but only by making mutually consistent decisions. <br/>In contrast, an obligation standard (enforced by law as "''[[de jure]]'' standard") is a solution to the [[prisoner's dilemma|prisoner's problem]].<ref name="Ulmann" />