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?

Sure , I ' d be happy to help you with your game theory exercise . In the Rock - P aper - Sc iss ors game , each player has three possible actions : Rock , P aper , or Sc iss ors . The pay offs for each action are as follows : \n \n * Rock be ats P aper \n * P aper be ats Sc iss ors \n * Sc iss ors be ats Rock \n \n To find the Nash equilibrium strateg ies for this game , we need to consider the following : \n \n 1 Each player has a best response to the other player ' s strategy \n * No player can improve their pay off by un il ater ally changing their strategy \n \n Let ' s start by analyz ing the game tree . The game tree for Rock - P aper - Sc iss ors has three branches , one for each action . At each node , there are three possible actions for the oppon ent , and each action has three possible actions for the current player . The game tree can be represented as follows : \n ``` css \n Rock \n / \ \n / \ \n P aper Sc iss ors \n / \ / \ \n / \ / \ \n P aper Sc iss ors Rock \n ``` \n To find the Nash equilibrium strateg ies , we need to identify the strateg ies that are best responses to each other . \n \n * For Rock , the best response to P aper is Sc iss ors , and the best response to Sc iss ors is Rock . \n * For P aper , the best response to Rock is Sc iss ors , and the best response to Sc iss ors is P aper . \n * For Sc iss ors , the best response to Rock is P aper , and the best response to P aper is Sc iss ors . \n \n There fore , the Nash equilibrium strateg ies for Rock - P aper - Sc iss ors are : \n \n * Rock : Best response to P aper is Sc iss ors , best response to Sc iss ors is Rock . \n * P aper : Best response to Rock is Sc iss ors , best response to Sc iss ors is P aper . \n * Sc iss ors : Best response to Rock is P aper , best response to P aper is Sc iss ors . \n \n Th ese are the only Nash equilibrium strateg ies for Rock - P aper - Sc iss ors , as no player can improve their pay off by un il ater ally changing their strategy . </s>