Questions tagged [nash-equilibrium]

A basic solution concept in game theory that requires each player to select their best response to the strategies chosen by others.

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476 views

Is there a systematic approach to find equilibria in sequential games?

I know that one can use backward induction to find one particular subgame perfect NE. And I know that wherever possible one can represent the game in normalform and then find all NE. But is there a ...
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1answer
173 views

Is there a term for a game whose pareto optimal solutions and nash equilibria are disjoint?

Is there a term for a game whose pareto optimal solutions and nash equilibria are disjoint? (e.g. prisoner's dilemma)
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Fehr-Schmidt, Ultimatum game, Subgame-Perfect Nash Equilibrium

I'm studying the different variations of the ultimatum games. I've spent some time on this following game: Assume now that each player does not only care about the amount of money she receives, but ...
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34 views

Nash in demand functions!

I am searching for some types of games that are played in linear demand functions. Altough I hear that there is a vast literatrure for games that are played in the intercept or the slope of the demand ...
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165 views

If a mixed strategy is strictly dominated, then there is a strictly dominated pure strategy in its support?

I am looking at the proof of NE survives the iterated removal of strictly dominated strategies (MWG, ex 8.D.2) and in the solution manual, authors say something like if a mixed strategy is strictly ...
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1answer
281 views

Tit-For-Stat Strategy Best Replies

Let $\delta\in(0,1)$ be the discount factor. Consider the stage game in the infinitely repeated prisoner's dilemma game: The goal is to derive conditions on $\delta$ such that the symmetric tit-for-...
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221 views

Subgame Perfect Equilibrium with Pure Strategies in Sequential Games [closed]

If I have a sequential game, i.e. in each node (that I will call $t$) only one player choose an strategy from a finite space of strategies, Is it true there always exist a subgame perfect equilibrium ...
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68 views

Equilibria for multi-round 'Markov' games?

I'm interested in zero-sum symmetric games which have the following form. Each player has a counter which starts at 0. Each turn, a player may choose from a fixed set of actions. A player's counter is ...
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63 views

Symmetric Nash Equilibrium in Stahl (1996)

Let $F(p)$ denote the distribution of prices in a market, $\pi(p, F)$ are profits choosing $p$ given distribution $F$. $E\pi(p,F)$ is defined to be $$ E \pi(p, F) = R(p) \psi(p, F)$$ where $R(p) = p ...
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1answer
332 views

How to demonstrate that a game always have a subgame-perfect equilibrium in pure strategies?

If I have an specific extensive game, with only a finite set of strategies, how can I demonstrate that the game always have a subgame-perfect equilibrium in pure strategies? My first intuition was to ...
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66 views

Is there really a Nash equilibrium in this example?

I was watching this video on Coursera and worked out the example before the solution was presented. The example begins at 4:20 The presenter says that the Nash ...
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2answers
112 views

Subgame Perfect Equilibrium for Pure and Mixed strategy

In a game theory textbook there is something similar to the table below where there is one pure strategy nash equilibrium and multiple mixed strategy nash equilibria. It is a simultaneous game with ...
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64 views

Game Theory: Continuity in equilibrium profits?

Consider 2 agents $A_i$. $A1$ moves before agent $A2$. Each of their utility functions is continuous in each agents' decision $0<s_i\in \mathbb{R}$ and a parameter $x$. Additionally, each agent's ...
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65 views

What does these "strategy notations" mean?

In a sequential game, where there are 8 pizzas. Player 1 decides number of pizzas he wants. Let's call it S1 (strategy of player 1), and S1 = 5 means player one decided to get 5 pizzas. Then player ...
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1answer
41 views

Strong sequential equilibria and the existence of others

I am working on the following game and I have to find all strong sequential equilibria here. I determined that here any belief derived from a fully mixed strategy gives a distribution (1/2, 1/2) over ...
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4answers
181 views

Doubt about Mixed Strategy Nash Equilibrium

Here's the video I will be referring too. Now I am a complete beginner in game theory, so sorry if this sounds like a stupid question, but why would a player want to balance out the payoffs of another ...
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2answers
2k views

Nash Equilibrium and Dominant Strategy

If I have a game that goes as follow: Player 1 is the row player and player 2 is the column player. I think that the Nash Equilibria should be (10, 5) and (5, 10), since neither of the player has ...
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1answer
61 views

Differences between best response, dominant strategy and Nash equilibrium

I can't seem to get the differences of these terms. I watched this video that has the differences of best response and Nash equilibrium: But then I heard about dominant strategies from another video ...
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1answer
49 views

Can't find the SPNE

For a homework assignment, I need to find the subgame perfect equilibrium. The assignment asserts that there is only one subgame perfect equilibrium in this problem, but I am stuck between two ...
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1answer
61 views

Non-negative deviations from Nash Equilibrium

I know that in a Nash Equilibrium, no player can profitably deviate from the equilibrium strategy assuming that the strategies of the other players remain the same. My question is, what if a player ...
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1answer
48 views

If a best-response dynamic converges, does it converge to a Nash equilibrium?

Consider a game with a finite number of players and finite action space. Suppose we consider a sequential iterative game-playing process in which, in each period, players myopically select actions ...
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1answer
40 views

Rationalizable strategies and Weak Dominance

Can I find the rationalizable strategies for a game where none of the players has strict dominance but only weak dominance?
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1answer
51 views

Pure and Mixed Nash Equilibrium algorithm gives different results

I have a game represented by following table: It is clear that there is a pure Nash equilibrium at 4,2 (both players do not cooperate, player 1 awarded 4 points and player 2 awarded 2 points). Now ...
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1answer
78 views

How to find mixed optimal strategies in this zero-sum game?

I'm trying to solve this problem from last year final exam in game theory: Consider the zero-sum game $G=(X, Y, g)$ where $X=Y=[0,1]$, and $$\forall (x,y) \in X \times Y: g(x, y)=\max \{x(1-2 y), y(1-...
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1answer
47 views

How would a 2D model of Hotelling's law outweigh the benefits of a 1D model?

I'm not sure if this goes here, or on a math exchange. I could move it if you guys want... Let's examine Hotelling's law on a 1D plain with two shops. Both shops would do society a favour if placed ...
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1answer
33 views

I cannot find for this Simple shared effort level game

Each player can contribute to the project with non-negative effort. Player 1's utility is $u_1=e_1(1+e_2-s\cdot e_1)$ where $s\in [0,1]$. Player 2's utility is $u_2=e_2(1+e_1-e_2)$ For case 1, ...
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1answer
59 views

Nash Equilibria in Target Destroying-Guarding Game

Army A has a single plane which can strike one of three possible targets, A, B and C. Army B has one anti-aircraft gun that can be assigned to one of the three targets to guard it. The value of each ...
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2answers
236 views

Compute Nash Equilibrium in median voter game

Consider a spatial model in which two candidates A and B compete for office. The policy space ranges from -1 to 1 and each candidate can take one of three positions, -1, 0, and 1 (so that they have ...
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1answer
5k views

Calculating Nash Equilibrium prices for Bertrand duopolists

I am attempting to solve the following problem. Suppose that firms' marginal and average costs are constant and equal to c and that inverse market demand is given by $P = a - bQ$ where $a,b > 0$. ...
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1answer
191 views

Mixed Strategy Bayesian Nash Equilibrium

There was an exercise question regarding two players with two types each in a game theory class. The two players were assigned to do a team project together. The utility from doing the team project is ...
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1answer
30 views

Why do we need a restriction of a game to prove the given statement?

Consider a game $G$. We have to prove that is $s$ is a Nash Equilibrium of $G$, then it is also a Nash Equilibrium of the game formed by removing strictly dominated strategies of $G$. I looked at the ...
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1answer
46 views

Difference between equilibrium and k-rationalizability

I'm reading a Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications by Crawford, Costa-Gomes and Iriberri. They write the following: In two-person games, a ...
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1answer
190 views

Intuition behind a cournot duopoly nash equilibrium producing a higher output than a monopoly?

I am just wondering if someone could explain the descriptive, not mathematical intuition behind why a cournot equilibrium for a duopoly produces a higher level of output than a monopolist but lower ...
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1answer
1k views

perfect bayesian nash equilibrium is simply nash equilibrium

Is it true that for two player zero sum game, Perfect Bayesian Nash equilibrium is simply Nash Equilibrium? I am learning game theory and our lecturer does not explicitly cover it.
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Will the outcome of a game always be a Nash Equilibrium?

Consider this game between two players. This game has two Nash Equilibria: (U, C) and (D, R). Suppose we ask the players to play this game once. What should our prediction of the game's result be? If ...
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1answer
62 views

A question about Nash Equilibrium

I have some trouble with Nash Equilibrium. The specific question as follows. Suppose that there are $2N$ people in the village, of which $N$ residents live in the first district, and each person ...
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3answers
93 views

Maximum-support Nash equilibria in zero-sum games

Context: I would like to know how likely a player is to pick a specific action, provided that he plays optimally and the action is optimal. Phrased like this, the question is ill-defined. But is there ...
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58 views

Cournot competition subgame perfect Nash equilibrium with two products

QUESTION: Assume there are two types of products, labelled $l$ and $n$. Firms compete in the market by choosing which product to sell and then choosing the quantities. Let $Q_n$ and $Q_l$ denote the ...
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99 views

Take It Or Leave It Strategy: Social Optimum

Here is what I understood Using Backward Induction, I inferred that buyer offers a price, say, $P$ and the seller will sell only if $P \geq c(I)$. Setting the lowest possible Price that will ensure ...
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90 views

Prisoner's dilemma as a Bayesian one-shot game

What happens if we assume that there is incomplete information to the prisoner's dilemma game? For example, suppose we have the following matrix with the utilities $T>R>P>S$ and $2R>S+T$ ...
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65 views

Deviating from Cournot-Nash

Suppose player $1$ and $2$ are playing a simultaneous move game where with continuous strategies $x_1$ and $x_2$. The Cournot equilibrium is $x_1^*,x_2^*$. The following diagram purports to show that ...
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Reference for truthful Nash on cartesian domain implies strategy-proofness

Consider a mechanism $M: \mathcal{R} \rightarrow X$, where $\mathcal{R}$ is a domain of preference profiles $R = (R_1,\dots, R_n)$, and $X$ is a set of outcomes. I believe that the following is a ...
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Why must the wage barganing be derived at steady-state?

In wage bargaining theory, in the context of matching theory, firms and workers can negotiate a Nash equilibrium by maximizing a function of firms' and workers' surplus - with the purpose of allowing ...
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91 views

Menu-pricing with three consumer groups

I want to analyze the following setting: An entrepreneur (with monopoly power) sells a product in two periods. In period 1 there are two consumer groups (denoted by 1 and 2) and in period 2 there is ...
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987 views

how to find Cournot equilibrium for 2 firms having different MC?

When MC function is different for both the firms, how will MR = MC work ?
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Can't solve this matrix for Nash Equilibrium?

So, I have the following 9 by 9 probability matrix. I want to solve it for a nash equilibrium. https://docs.google.com/spreadsheets/d/16Y1FqxRIAHsHpgEz1ckxDt2sEOInOG3zz_wU8kBHvB4/edit?usp=sharing For ...
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Is the symmetric equiblirium in congesstion games always inferior in terms of social-welfare?

Let $G$ be a finite, symmetric, congestion game. According to Nash theorem, a (mixed) symmetric equilibrium surely exists. Congestion games also known to admit pure-strategies Nash equilibrium as they ...
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186 views

Existence of pure strategy Nash equilibrium

I understand the reason why mixed strategy Nash equilibrium exists. But what are the conditions for the existence of pure strategy Nash equilibrium?
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270 views

Mixed Nash equilibrium

I have game table posted below: $$\begin{matrix} &\#2 \\ \#1 & \begin{array}{c|c|c|c} &D &E &F \\ \hline A &4,4 &6,6 &2,6 \\ \hline B &6,4 &2,2 &0,4 \\ \...
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Subgame-perfect Nash equilibrium perfect information

This might be a stupid question but please bear with me. I'm trying to solve this game but I'm in doubt on how to represent the strategy profile of the game. The game looks like this in extensive-form....