microeconomics-game theory

MICROECONOMICS- GAME THEORY (Microeconomics- Game theory (Page 1

Q1 (a . Players : The players are two firms , Firm-1 and Firm-2 N 1 2

Strategies : The strategy set for firm-1 is F1 F , A in which F denotes that the firm decides to spend 1 million for developing new electronic hardware and A is vice-versa

Similarly strategy set for firm-2 is F2 F ,A where firm-2 decides whether to spend 1 million for development of software or not

F2 F A

F

10 , 5 -1 , 0 0 , -1

0 , 0 F1

A

The cells of the above matrix show the payoffs for both the companies under different circumstances (b . A pure strategy is a term used to refer to strategies in Game theory . Each player is given a set of strategies , if a player chooses to take one action with probability 1 then that player is playing a pure strategy . This is in contrast to a mixed strategy where individual players choose a probability distribution over several actions

is a Nash equilibrium (NE ) if no deviation in strategy by any single player is profitable , that is , if for all i The pure strategy Nash Equilibrium cells for the above matrix would be F , F and A , A (Ref . 1 (Microeconomics- Game theory (Page 2

If a game has a unique Nash equilibrium and is played among players with certain characteristics , then it is true (by definition of these characteristics ) that the NE strategy set will be adopted . The necessary and sufficient conditions to be met by the players are

Each player believes all other participants are rational

The game correctly describes the utility payoff of all players

The players are flawless in execution

The players have sufficient intelligence to deduce the solution

Each player is rational

These conditions signifies that there is a unique equilibrium . The game signifies that the unique playoff for all the players as seen above in the payoff matrix and other conditions are to be assumed for the unique equilibrium . Since each player is rational and have sufficient intelligence to deduce the solution , I expect that the two players would be satisfied with the outcome since either both the players would not invest in developing their products before prior agreement with each other or they will invest 1 million only after ascertaining that the other will also invest in building the complimentary product . If they both invest in their respective products then they will be able to earn huge profits . Moreover the double profit of firm 1 will not in any way hamper the growth of the firm 2 as they are not competitors and are in different branches of manufacturing

There are two equilibria from the firms prospective , one is F , F where 10 and 5 signify the payoff that firm 1 and firm 2 receive if they both agree to invest 1 million for manufacturing of their product . The other equilibria is A , A where 0 is the payoff for both the fiems if they donot...