Game Theory ( 2 player zero-sum game)

In summary, the conversation is about a game theory exercise involving a two-player zero-sum game and a minimax argument. The participants are discussing how to solve the exercise using a constant K and a new game matrix A0. They believe that the equilibrium solution (e1; e1) still holds for A0, but are unsure of the next steps. One participant has calculated e2TA1e1 and e2TA2e1, but is unsure of their accuracy and how to proceed.
  • #1
ruby_duby
46
0
Hi

I have just started a game theory module and have been given the following exercise. Can anyone help me with the following question. I have a feeling I can use a minimax argument to answer this but I am not sure how to go about this.

Suppose a two-player zero-sum game has the following matrix:
A =

a b
c d

Suppose that (e1; e1) is an equilibrium solution. Suppose K a member of the ℝ is a constant. Show for the new game matrix:
A0 =

a + K b + K
c + K d + K

that (e1; e1) is still the equilibrium solution.
 
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  • #2
if i let Suppose a two-player zero-sum game has the following matrix:

A1 =

a b
c d

then calculate e2TA1e1 = c

Then if I let A2 =

a+k b+k
c+k d+k

then e2TA2e1 = c+k

but I have no idea if this is right or what to do next
 

1. What is game theory?

Game theory is a branch of mathematics that studies the strategic decision-making process in situations where multiple players or agents are involved. It is used to analyze the possible outcomes and strategies of different games, including those in economics, politics, and social interactions.

2. What is a 2 player zero-sum game?

A 2 player zero-sum game is a game in which there are only two players and the total payoff is always zero, meaning that one player's gain is equal to the other player's loss. This type of game is also known as a strictly competitive game, as the interests of the two players are completely opposed.

3. How is game theory used in real-life situations?

Game theory is used in a variety of real-life situations, such as in business negotiations, political campaigns, and military strategy. It helps decision-makers to understand the potential outcomes of different strategies and make more informed choices in complex situations where there are multiple players with conflicting interests.

4. What is the difference between cooperative and non-cooperative games?

In cooperative games, players can communicate and make binding agreements with each other, while in non-cooperative games, players cannot communicate and must make decisions independently. In game theory, cooperative games are studied using cooperative game theory, while non-cooperative games are studied using non-cooperative game theory.

5. Can game theory predict the outcome of a game?

No, game theory cannot predict the outcome of a game with certainty. It can only provide a framework for understanding the potential outcomes and strategies of different games. The actual outcome of a game also depends on factors such as the players' abilities, their level of rationality, and any random elements involved.

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