# Tagged Questions

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### A little question about payoff functions being continuous.

In the mixed extension of a finite game $G$, why are the payoff functions of players continuous? Does it has something to do with being von Neumann and Morgenstern utility functions? Is there other ...
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### Pure vs mixed strategy Nash Equilibria

Just learning about Nash Equilibria. The pure strategy one is explained as an outcome where both/all players feel like they couldn't have done better given what the others were doing. Mixed strategy ...
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### Finding Nash Equilibria of a finte game of 2 players.

In a finite game, suppose player 1 has strategies $\{\alpha_1,\alpha_2\}$ and player 2 $\{\beta_1,\beta_2\}$ with payoffs as below. \begin{array}{c|c|c} &\beta_1&\beta_2\\ \hline\\ ...
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### Finding mixed Nash equilibria in continuous games

I'm taking my first (graduate-level) game theory class. I understand how to find Nash equilibria in simple games, such as those given in finite tables, and can see (usually) how to find the mixed ...
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### Are all Nash equilibrium pure strategies also Nash equilibrium mixed strategies.

while going over wiki page on Battle of the Sexes game I found something funny. This game has two pure strategy Nash equilibria, one where both go to the opera and another where both go to the ...
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### Mixed Strategy Nash Equilibrium of Rock Paper Scissors with 3 players?

It seems like most game theory tutorials focus on 2-player games and often algorithms for finding Nash equilibria break down with 3+ players. So here is a simple question: Is ...
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### Analytically solving (calculating Nash equilibrium for) 3-player extensive form games

Let's say we extend the popular half-street Kuhn poker variant to 3 players. The rules would be as follows: ...
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### Can the Nash bargaining solution be applied in repeated game?

I am trying to develop a model involving two agents who interact strategically to set an optimal time for a joint work. These agents will have to meet repeatedly. I want to derive the optimal time for ...
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### Does chess have more Nash equilibria than you can find through backwards induction?

All equilibria found with backwards induction on a tree of a perfect information game are Nash equilibria, but in general the reverse is not true: ...
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### vickery auction question(second-price auction)

The question is as follow, Alice and Bob would both like to own the same manuscript. The manuscript is worth 5 million to Alice and worth 3 million to Bob. The present owner of the manuscript ...
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### Correlated Equilibrium - Transforming a non-linear objective function into a linear one

I am trying to transform a non-linear objective function into a linear one, in order to create a LP. How might I go about to do this (I have never taken a course in linear programming). I have that I ...
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### subgame perfect nash equilibrium for war of attrition

the question is as follow: suppose that two players are playing war of attrition, that means both of them could choose either to fight or quit, if either one of them quit, the game ends, and if ...
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### cournot competition with N-firms

The question is as follow: Here is how we can think of N-firm Cournot competition. Assume all the firms have the same marginal cost C > 0. Firm 1 chooses Q1, Firm 2 chooses Q2, and so on. The market ...
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### cournot equilibrium and stackelberg equilibrium question

Question is as follow: there are 2 firms that want to enter the apple juice market in country A. There are no existing firms in the market or potential entrants. They need to decide on yearly ...
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### mixed strategy nash equilibrium question!

Suppose the game consists of only $2$ players, player $1$ and player $2$, and each of them has only $2$ strategies to choose between. This gives a $2$ by $2$ payoff matrix. Player $2$ has no ...
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### Question on mixed nash equilibrium!

The question is as follows: Think of the Golden Ball game. Now player 1 is money-minded and jealous, and player 2 is very good-hearted, so the payoff matrix is follows: ...
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### Is equilibrium selection in zero sum game trivial?

Does a zero sum game always has a unique payoff, whatever the nash equilibrium selected is ? even with mixed strategies ? If so, what is the proof ?
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### Subgame Perfect Nash Equilibrium

My homework question is summarized below: There are 7 players (say P1,P2,...,P7) trying to split 100 dollars. The game starts with P1 proposing an allocation of the 100 dollars to each ...