I have an exercise in game of theory class that I should find all equilibriums in rock paper scissors game. Could you help me with this exercise?

Of course , I ' d be happy to help you with your game theory exercise ! \n To find the equilib ri ums in a Rock - P aper - Sc iss ors game , we need to analyze the strateg ic interactions between players . In this game , each player has three possible actions ( R ock , P aper , or Sc iss ors ), and each action can beat one of the other two actions . \n An equilibrium is a set of strateg ies that no player can improve upon by un il ater ally changing their strategy . In other words , if all players choose their strateg ies optim ally , no player can gain an advantage by changing their strategy . \n To find the equilib ri ums in this game , we need to identify all possible pairs of strateg ies that are Nash equilib ria . A Nash equilibrium is a strategy profile such that no player can improve their pay off by un il ater ally changing their strategy , assuming all other players keep their strateg ies un changed . \n Here are the possible pairs of strateg ies that are Nash equilib ria in a Rock - P aper - Sc iss ors game : \n 1 . Rock - R ock : Both players choose Rock , which be ats P aper and Sc iss ors . This is a dominant strategy equilibrium , meaning that either player can improve their pay off by choosing Rock . \n 2 . P aper - P aper : Both players choose P aper , which be ats Rock and Sc iss ors . This is also a dominant strategy equilibrium . \n 3 . Sc iss ors - Sc iss ors : Both players choose Sc iss ors , which be ats Rock and P aper . This is also a dominant strategy equilibrium . \n 4 . Rock - P aper - Sc iss ors : This is a mixed strategy equilibrium , where each player cho oses one of the three actions with probability 1 / 3 . This equilibrium is stable because no player can improve their pay off by changing their strategy , assuming the other player ' s strategy is fixed . \n So , there are four equilib ri ums in a Rock - P aper - Sc iss ors game : Rock - R ock , P aper - P aper , Sc iss ors - Sc iss ors , and Rock - P aper - Sc iss ors . \n I hope this helps you with your exercise ! Let me know if you have any questions or need further clar ification . </s>