<P> A symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them . If the identities of the players can be changed without changing the payoff to the strategies, then a game is symmetric . Many of the commonly studied 2 × 2 games are symmetric . The standard representations of chicken, the prisoner's dilemma, and the stag hunt are all symmetric games . Some scholars would consider certain asymmetric games as examples of these games as well . However, the most common payoffs for each of these games are symmetric . </P> <P> Most commonly studied asymmetric games are games where there are not identical strategy sets for both players . For instance, the ultimatum game and similarly the dictator game have different strategies for each player . It is possible, however, for a game to have identical strategies for both players, yet be asymmetric . For example, the game pictured to the right is asymmetric despite having identical strategy sets for both players . </P> <Table> <Tr> <Td> </Td> <Td> </Td> <Td> </Td> </Tr> <Tr> <Td> </Td> <Td>--1, 1 </Td> <Td> 3,--3 </Td> </Tr> <Tr> <Td> </Td> <Td> 0, 0 </Td> <Td>--2, 2 </Td> </Tr> <Tr> <Td_colspan="3"> A zero - sum game </Td> </Tr> </Table> <Tr> <Td> </Td> <Td> </Td> <Td> </Td> </Tr>

Who won a nobel prize in economics for his work in the development of game​ theory