Conflicts in the choice among Nash Equilibria

4.13 of The Economy 1.0 & The Economy #3

What does a Nash Equilibrium entail?

-Set of strategies, one for each player in the game, such that each player’s strategy is a best response to the strategies chosen by everyone else
-Can be seen as a good enough prediction to what may occur

-Why is there two Nash Equilibria here?

-If Bala chooses rice, Anil’s best response is to grow cassava. If Bala chooses Cassava, Anil’s best response is to grow rice

-Same occurs with Anil

-Therefore, two Nash Equilibria exist here, and crucially, both outcomes are not the same - one is clearly more favourable

When two (or more) Nash Equilibria exist, what questions should be posed?

-Which equilibrium should be most likely to be seen?

-Is there a conflict of interest because, in equilibrium is preferable to some players, but not to others?

Why is John Nash (1928-2015) seen as a great economist?

-As his surname hints, he came up with Nash Equilibrium, which helped advance Game Theory to another level

-Nash managed to prove that any game with x amount of players, with y amount of strategies, must have at least one equilibrium, given that players can randomise freely.

-For example: Chess: It is a finite game, there are finite players, and in theory, there is a Nash Equilibrium out there - what that is, no one knows yet.

-Using this, what can be immediately worked out? (Assume that C++ means more pay)

-They both do better if they work in the same language

-Astrid likes Java, Bettina likes C++

-Their total payoff is highest when they both code with C++

-Given these payoffs, where are the Nash Equilibria, and would they ever switch over?

-Here, there exist two Nash equilibria: both coding with Java or C++.

-It is already impossible to tell, with certainty, which outcome will happen, but assuming they both code with Java, then any deviation from one leads to a worsening in their circumstances. Therefore, there is zero incentive to change

Only a change in the rules of a game may lead to a certain ending