# Tagged Questions

0answers
38 views

### Nash equilibria in 3-player game

Consider 3-player game. Players $x,y,z$, each player has two strategies. $x$: $x_1$ and $x_2$, $y$: $y_1$ and $y_2$, $z:z_1$ and $z_2$. The outcome of the game are represented by the triple ...
3answers
73 views

### nash equilibirum help! seems tricky

Any advice for finding all nash equilibrium for this symmetric game? (B,B) looks like one but I feel like there are more. I tried looking for strictly dominant strategies, but only A weakly dominates ...
1answer
42 views

### Is there an example of zero-sum game that has a Nash equilibrium which is not subgame perfect?

As a refinement of Nash equilibrium, it is known that not all Nash equilibria are subgame perfect. But it seems to me in zero-sum games of perfect information, Nash equilibrium coincides with subgame ...
0answers
25 views

### Algorithm to verify that a weak Nash equilibrium is an ESS, or a strict Nash equilibrium

Is there any algorithm that might assist me in checking whether a weak Nash equilibrium in a signalling game is also an Evolutionarily Stable Strategy, or a strict Nash?
0answers
50 views

### Game theory: Efficient and stable mechanisms

I am having some trouble understanding the notion of efficient and stable mechanisms in game theory. Could someone explain both concepts informally?
1answer
29 views

### Question on the construction of mapping from space of strategy profile into itself in Nash(1951)

To appeal to Brouwer fixed point theorem, Nash(1951) constructed a continuous mapping $\operatorname{T}$ from strategy profile space into inself: For player $i$, the probability of a pure strategy ...
0answers
64 views

### Unexpected hanging paradox maxmin strategies

I have a question about strategies of the players of Unexpected hanging paradox (I am very sorry for a long topic, topic exist already for a while, during this time I try to develop idea how to solve ...
1answer
98 views

### Finding the payoff matrix of a game

A two player zero-sum game can be represented by a $m\times n$ payoff matrix $M$ having $m$ rows and $n$ columns with values in $[0,1]$. The value $M(x,y)$ represent the payoff given to player $1$ ...
2answers
114 views

### Cournot-Nash Equilibrium in Duopoly

This is a homework question, but resources online are exceedingly complicated, so I was hoping there was a fast, efficient way of solving the following question: There are 2 firms in an industry, ...
1answer
38 views

### Theorem that stable equilibria in iterated games are equivalent to coalition-based static equilibria

Consider an $n$-player nonzero sum finite game $G$. I have a vague recollection of a wonderful paper proving an equivalence between (1) steady state Nash equilibria of $G$ played countably many times ...
1answer
232 views

### Nash equilibria and best response functions

a) Let $G=(A,u)$ be a strategic game such that, for each $i \in N$ $A_i$ is a nonempty, convex, compact subset of $R^{m_i}$ $u_i$ is continuous For each $a_{-i}$, $u_i(a_{-i}, . )$ is quasi-concave ...
1answer
127 views

### Prove set of Nash equilibria is closed?

Is this even possible with just the formal definition of a Nash equilibrium, that is, without any additional conditions, such as the utility function is continuous? Thanks.
2answers
108 views

### What is the Nash Equilibrium of the Monty Hall Problem?

The Monty Hall problem or paradox is famous and well-studied. But what confused me about the description was an unstated assumption. Suppose you're on a game show, and you're given the choice of ...
0answers
73 views

### Comparing Nash equilibrium and Pareto optimal actions

Suppose that $(x_{i}, x_{j})$ identify actions for two players $(i,j)$. If we define Pareto optimal actions by $$h(x_i) +h(x_j)- \eta[p(x_i)+p(x_j)]=2\gamma$$ and Nash equilibrium actions by ...
1answer
125 views

### 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 ...
2answers
188 views

### 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 ...
0answers
243 views

### 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 ...
0answers
255 views

### 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: ...
0answers
45 views

### 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 ...
2answers
178 views

### 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: ...
1answer
67 views

### 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 ...
1answer
39 views

### 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 ...
1answer
77 views

### 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 ...
2answers
761 views

### 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 ...
1answer
529 views

### 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 ...
1answer
95 views

### 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 ...
1answer
122 views

### 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: ...
2answers
63 views

### 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 ?
2answers
398 views

### 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 ...
1answer
244 views

### Iterated prisoners dilemma with discount rate and infinite game averages

Suppose we have two players who are perfectly rational (with their perfect rationality common knowledge) playing a game. On round one both players play in a prisoners dilemma type game. With payoffs ...
1answer
211 views

### Finding Nash Equilibria with Calculus

The problem is summarized as: There are two players. Player 1's strategy is h. Player 2's strategy is w. Both of their ...
1answer
284 views

### Unable to find Nash equilibria in mixed strategies

Here is the strategic form game: Player 2 Left Middle Right Top 2,2 0,0 1,3 Player 1 Middle 1,3 3,0 1,0 ...
0answers
52 views

### what exactly does symmetric game and symmetric equilibrium mean?

I am confused about the ideas of a symmetric game and symmetric equilibrium of a game under the following conditions. 1) pure strategy Nash equilibrium 2) Nash bargaining game where players set a ...
1answer
802 views

### Mixed-strategy Nash equilibria

I didn't find in books, so I'm asking - Mixed-strategy Nash equilibria is always only one or doesn't exist for the one certain game? And I know that there can be several(and can not be at all) pure ...
1answer
154 views

### Find the Nash Equilibrium for a Cournot Game

Consider a Cournot game with $2$ firms. Firm $i$ has constanct marginal cost $C_i$, where $C_1 \lt C_2$. Inverse demand is linear: $p(q)=A-q$ (where $A \gt 2C_2 - C_1$). Find the Nash Equilibrium.
2answers
122 views

### Am I correct in thinking this game has neither Nash Equilibria nor dominant strategies?

I've taken this example from some lecture slides. The slides state there is no Nash equilibrium. I suspect there is also no dominant strategy for either player. Is this true? Two players $i$ and $j$ ...
1answer
72 views

### Nash equilibria of mixed strategies

I am given the following game to find nash equilibria in pure and mixed strategies: \$\begin{pmatrix}& & Litte John &\\ & & c & w \\Big John & c & (5,3) & (4,4) \\ ...
2answers
1k views

### Cournot Nash Equilibrium Between Two Firms

Suppose we have two firms with specialized, but similar products. Suppose market demand for the two products is: $$p_1(q_1,q_2)=a-bq_1-dq_2$$ $$p_2(q_1,q_2)=a-bq_2-dq_1$$ where $d \in (-b,b)$. Suppose ...
1answer
289 views

### Finding Nash equilibria using Support Enumeration

Chapter 3 of the Book "Algorithmic Game Theory" introduces an algorithm (page 8 of that PDF) to find mixed Nash equilibria for a bimatrix game $(A, B)$, which I struggle to understand. ($M$ and $N$ ...
1answer
117 views

### Mixed strategy nash equilibria in from 2xN bimatrix form

I'm looking for a way of finding (manually!) mixed strategy Nash equilibria in a 2xN game. Calling player 1 the player with two strategies and player 2 the one with N strategies, I've constructed ...
1answer
135 views

### Apply game theory/Nash equilibrium in computer security scenario

I want to apply the game theory to a scenario in security . where two ppl the optimal outcome of a game is one where no player has an incentive to deviate from his or her chosen strategy after ...
1answer
220 views

### Meaning of a partial derivative here?

I am given a 'tariff' function for two countries, $i=1, 2$. Both players can select a tariff between 0 and 100. If player $i$ selects $x_i$ and player $j$ selects $x_j$, country $i$ gets a payoff of ...
1answer
250 views

### Finding Nash equilibrium aka finding where lines intersect

I am tagging this as multivariable calculus because it potentially involves taking partial derivatives. I am working on some mathematical treatment for Cournot duopoly models (not homework, just ...
1answer
172 views

### Algebraically finding a Nash equilibrium

Here's the problem that relates to a whole class of problems to which I am trying to figure out a general solution. Given two players 1 and 2 who can select a number from the interval $[0, 1]$, ...
3answers
219 views

### Is there experimental evidence that people ever play mixed Nash equilibrium in real games?

Have any studies been done that demonstrate people (not game theorists) actually using mixed Nash equilibrium as their strategy in a game?
2answers
224 views

### Newspaper competition

A newspaper launches a competition. It said that readers should submit one number between 1 and 1000. A £2000 prize would be awarded to the person that got the closest to 2/3 of the mean of all the ...
1answer
865 views

### Symmetric nash equilibrium

I was reading this paper on position auctions for web ads. Basically, there are N slots each with an expected number of clicks (in a particular time period) $x$. Each agent makes a bid $B_i$ of how ...
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