Question 3: Description of an Economy Consider an endowment economy populated by

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Question 3: Description of an Economy Consider an endowment economy populated by Ben and Jerry. They live at t 0,1 and are exposed to the risk of weather change. At t = 1, the weather will be either sunny or rainy with equal probabilities. Their lifetime endowments are represented by three dimensional vectors, (eo,e, (rainy), e(sunny). In those endowment vectors, eo indicates the quantity of goods given at period 0, e (suuny) that given at period 1 if sunny, and e, (rainy) that given at period 1 if it rains. Ben's lifetime endowment is represented as vector of (1, 0, 2) whereas Jerry's endowment as (1,2,0).Note thatthose endowments cannot be stored. As for preferences, Ben and Jerry hold an identical utility function U(co,e,(rainy),c,(sunny)) logco Blogc, sunny)lo(rainy),0

Explanation / Answer

In game theory, the Nash equilibrium, named after the late American mathematician John Forbes Nash Jr., is a solution concept of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.[1] If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitutes a Nash equilibrium. The Nash equilibrium is one of the foundational concepts in game theory. The reality of the Nash equilibrium of a game can be tested using experimental economics methods[citation needed].

Stated simply, Alice and Bob are in Nash equilibrium if Alice is making the best decision she can, taking into account Bob's decision while Bob's decision remains unchanged, and Bob is making the best decision he can, taking into account Alice's decision while Alice's decision remains unchanged. Likewise, a group of players are in Nash equilibrium if each one is making the best decision possible, taking into account the decisions of the others in the game as long as the other parties' decisions remain unchanged.

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