a) Suppose there are three ice cream sellers that locate simultaneously. Find the Nash equilibrium is there is one. Else, explain why there is none. (Focus on pure strategy Nash equilibria)
In game theory, Harold Hotelling discovered the location game, which is frequently referred to as Hotelling's location game.
We should presume rationality in game theory since we rarely see it in real life. The term "rationality" is a broad one.
A player or agent is rational, according to game theorists, if he or she is aware of all possible outcomes. As a result, participants realize they are rational. In the placement game, both ice cream vendors chose the middle spot.
In this game, the rationality of each participant is clearly recognized. Because they are rational participants, ice-cream seller A and ice cream seller B do not choose the endpoints. Player A will not choose a dangerous place for herself, and Player B will not choose a hazardous location for him.
So, if the players are completely aware of one another's rational behavior, they are mutually reasonable, and they will choose the median place, like in the case of ice cream vendors. Despite the fact that the players are rational by nature, they choose to play Nash equilibrium rather than rationally in the location game. As a result, I believe that firms and customers will behave irrationally.
As a result, we should not assume rationality in game theory because it is rarely observed in actual life.