Multiple Equilibria in Pure Strategy:

Although many examples provided in  this unit so far give the  impression that each game has a single solution, it  is possible that  there may be situations in which  two or more possible equilibria exist in a game. The following game  is an example of such situation.

Example:

Suppose, two nations, for example,  United  States  of  America (USA)  and Russia, have two choices  in  front of  them  either  to  build more wea.pons  or refrain from doing so. The best outcome for each is when neither builds -  the balance  of  power  is  maintained  and  the  resources that  would  have  gone  to armaments can instead be  deployed  to  improve the standard of  living of the citizens.  In  that  case, each of the countries has  the  payoff of four. The worst outcome  for each country rated 1, is  the  situation  in which  it  refrains but  the other builds. The  outcome  in  which both build  is  rated  2  by  each of them. Each gives a  rating of 3  in  which  case  it  builds and the other refrains. The game is depicted by the following table.  

Both  the countries would  clearly prefer  the equilibrium  in which both refrain but  that does  not automatically ensure that  each will  choose  the  refrain strategy while  playing  the game. If one player  thinks that the other for some reason will  choose 'build',  then  it  should choose build  too. To be induced  to choose refrain, what each really  needs  is the assurance that the other will also choose  refrain.  Therefore, these types  of  games  are  often  called  assurance games.