Question

Questlon 2 1S0 marks) Considera oftwareindustry populated by n companies which ane indexed by i-1,2,., n. Developer i has an ideal specification 0, E R, which is an exogenous parameter. When developing its software the company wishes to select its specification parameter St E R, as close as to the ideal specification e. Developers also would like their products to be compatible with other software, i.e. company i wants its specification s to be as close as possible to other specifications, s,. The payoff of company i is given by u(s) 10 (s -)2 n -1 ini Note that a developer pays two "costs": one for being away from the ideal specification 8, captured by the term -(s-0)2, and one for being away from the specification of other software, captured by the expression in the summation sign. Formulated as a game, the software developers are the players, they simultaneously pick their specifications, the game is played once, and the vector (0, ,%) as well as the above payoff function are common knowledge. Obtain the Nash equilibrium in this simultaneous-move, one-shot game.

Answer 1

Every developer is better off by choosing the closest to its ideal specifications. Hence, the entire payoff matrix will be reduced to

$ui(\theta 1, \theta 2....\theta n)= 10-\sum (\theta i - \theta j)^2 /n-1; j\neq i; j=1$

On further calculation we can see that the NE will be obtained for minimum values for difference between the ideal specifications, with no other strategy providing a better alternative except in the scenario where all the ideal specifications are simulataneously similar.

In that case, ui=10

else, it will be equal to above formula