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50<br />

perfect <strong>in</strong>formation <strong>and</strong> imperfect <strong>in</strong>formation games; peace <strong>and</strong> war game, <strong>and</strong> coord<strong>in</strong>ation<br />

game. Game <strong>the</strong>ory analyzes <strong>the</strong> available choices <strong>and</strong> possible outcomes as well. Game <strong>the</strong>ory<br />

when applied to <strong>the</strong> study <strong>of</strong> IGOs-states relations, it helps to underst<strong>and</strong> <strong>the</strong>ir actions <strong>and</strong><br />

<strong>in</strong>teraction. This <strong>the</strong>ory is also aimed to simplify <strong>and</strong> to solve problems faced by <strong>in</strong>ternational<br />

actors by assist<strong>in</strong>g states <strong>and</strong> IGOs <strong>in</strong> situation analysis <strong>and</strong> <strong>in</strong> tak<strong>in</strong>g rational decisions. The<br />

application <strong>of</strong> Game <strong>the</strong>ory <strong>in</strong> <strong>the</strong> study <strong>of</strong> IGO is not very common however it will make its<br />

place with <strong>the</strong> passage <strong>of</strong> time.<br />

3.5.1.1 Coord<strong>in</strong>ation game <strong>the</strong>ory<br />

The concept <strong>of</strong> coord<strong>in</strong>ation games is widely used <strong>in</strong> social sciences <strong>in</strong> order to study <strong>the</strong><br />

situations <strong>in</strong> which actors, <strong>in</strong>dividuals or groups drive mutual ga<strong>in</strong>s through mutual decisions.<br />

Coord<strong>in</strong>ation game is a type <strong>of</strong> cooperative games <strong>and</strong> presents <strong>in</strong>teraction between <strong>in</strong>dividual or<br />

grouped players: states <strong>and</strong> IGOs. In coord<strong>in</strong>ation games players are free to choose <strong>the</strong> same or<br />

correspond<strong>in</strong>g strategies, which result <strong>in</strong> multiple pure Nash equilibria: usually more than two<br />

Nash equilibria are <strong>in</strong>volved. In <strong>the</strong>se games <strong>the</strong> idea <strong>of</strong> a coord<strong>in</strong>ation problem is formalized<br />

<strong>and</strong> it concentrates on <strong>the</strong> possibilities for agreements. Coord<strong>in</strong>ation game is nei<strong>the</strong>r zero sum<br />

game nor sequential <strong>in</strong> nature. This game can be extended for more than two strategies <strong>and</strong> for<br />

more than two players but when applied to state-IGOs <strong>the</strong>re is always at least one IGO is present<br />

<strong>in</strong> <strong>the</strong> game while <strong>the</strong> o<strong>the</strong>r players or actors can be state/s. Pay<strong>of</strong>fs for each player- state or<br />

organization- depend on <strong>the</strong> choices available <strong>and</strong> <strong>the</strong> strategies adopted by both <strong>the</strong>ir own <strong>and</strong><br />

<strong>the</strong>ir opponents. Accord<strong>in</strong>g to Bryant coord<strong>in</strong>ation model for <strong>the</strong> pay<strong>of</strong>fs <strong>of</strong> each player can be as<br />

(Bryant, 1983)<br />

Where is <strong>the</strong> choice <strong>of</strong> player <strong>and</strong> is <strong>the</strong> vector <strong>of</strong> choices by o<strong>the</strong>r players, assum<strong>in</strong>g that<br />

are multiple Nash equilibria <strong>and</strong><br />

In <strong>the</strong>se cooperation base games each player takes an action <strong>in</strong> response to o<strong>the</strong>rs <strong>and</strong> selects a<br />

strategy to maximize his pay<strong>of</strong>f. Accord<strong>in</strong>g to Russell Cooper <strong>the</strong> strategy based pay<strong>of</strong>f for<br />

player can be written as,<br />

Where <strong>and</strong> is <strong>the</strong> strategy adopted by player <strong>and</strong> is <strong>the</strong> strategy adopted<br />

by o<strong>the</strong>r players than player (Cooper, 1999)

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