Questions tagged [nash-equilibrium]

For questions regarding the the Nash equilibrium solution concept in strategic games.

392 questions
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Nash equilibrium for Subgame Perfect Equilibrium? [on hold]

Is there a Nash equilibrium for a game that is not Subgame Perfect Equilibrium?
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Computational complexity of nash equilibrium in continuous games

What is the complexity of computing a Nash equilibrium (or as a decision version, does a pure strategy Nash equilibrium exist?) for continuous games with the following structure? Each player solves a ...
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Problem with Bayes-Nash equilibrium and correlated equilibrium

I'm trying to find the solutions for these two exercises: the first one involves this Hawk-Dove bimatrix I posted here: https://i.stack.imgur.com/SANvV.png In this game both players prefer the same ...
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Game Theory - Finding a Nash Equilibrium in Public Good Consumption.

Two players, 1 and 2, simultaneously choose their consumption of a public good. Given the consumption choices, g1 and g2, player 1 derives a marginal benefit of MB1 = 10 - (g1 + g2), while player 2's ...
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Can you find a winning strategy for this iterated prisoner's dilemma?

This platform allows to create a bot that plays the iterated prisoner's dilemma with other bots. There are some significant differences with the traditional setup: You can choose the bots you want ...
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What is the precise mathematical definition of what becomes a $n$ players game?

Question 1. What is the precise mathematical definition of what becomes a n players game in the context of game theory in which the Nash equilibrium theorem holds? An answer that is the indication of ...
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Mixed strategy Nash equilibria in $3×3$ games

I am confused as to how one would go about finding the Nash equilibria of a game like this. I know that it requires eliminating some of these strategies by showing that they are strictly dominated by ...
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What is the game in which both players are uninformed and have two types?

I understand the screening game and signaling game. What if both players are uninformed and have two types? What type of game is this and how do I find PBE?
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Three players mixed strategy nash equilibrium problem

The table above represents payoff for three players game accordingly. The probability for z1 is z and z2 is (1-z), r1 is r and r2 is (1-r) meanwhile for p1 is p and p2 is (1-p). Firstly, I would like ...
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Mixed Strategy Without an Option = Option is Dominated?

If a matrix game has a Nash equilibrium strategy in which certain options are not used (i.e. chosen with 0% probability), does that mean that those options are strictly dominated? If so, is it also ...
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Proof of the Existence of Bayesian Nash Equilibria

I found the following two Theorems when studying games with incomplete information. "Consider a ﬁnite incomplete information (Bayesian) game. Then a mixed strategy Bayesian Nash equilibrium exists." ...
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The Trust Game: what is the Nash equilibrium?

Here is how the experiment goes: Half of the participants were given the role of a first mover, and half that of the second mover. In each round, it was common knowledge that a first mover would be ...
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Best strategy in the game of Shoot-charge-dodge

The rules of the game are the following: There are 2 players, each of them have a gun and plays at the same time in every turn, in a turn they must perform one of three actions, shoot, charge or ...
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Mixed strategy equilibria

How do you find the mixed strategy equilibria from this game. Thank you. As ps strictly dominates qr, and once qr is eliminated, U* strictly dominates DA and DB, so this not suggest that there are no ...
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Lowest Unique Ordinal Game

The "lowest unique integer game" is widely-known: Some number of players each pick an integer from the range $[1, n]$ and the winner is the player who chose the lowest unique integer (if such a player ...
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Nash equilibrium that is not subgame perfect in an infinitely repeated game?

All of the literature on infinitely repeated games with perfect information uses the term subgame-perfect equilibrium. However, I cannot find any such game with a Nash equilibrium that is not subgame-...
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Mixed strategy equilibrium for subgame

A game has 3 players and the last player to move is player 3. In determining the subgame perfect equilibrium there is a subgame where player 3 has two choices and for each choice the payoff for that ...
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How to construct a 2-player normal form game with exactly n Nash equilibria?

Just like the title, how to construct a 2-player normal form game with exactly n Nash equilibria? Construct a NxN game with N pure NEs or we could also construct a 2x2 game with as many NEs as we ...
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Nash Equilibrium Grandfather Problem

A grandfather is writing his will and must decide how much money he will leave to his three children: Sean, Tom, and Brad. The grandfather comes up with the following plan. Each of his children is ...
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What is the Nash Equilibrium of the Dollar Auction?

The dollar auction is a type of auction in which players bid money for a dollar. Whoever bids the most pays what they bid and gets the dollar. Whoever bids the second most pays what they bid and get ...
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Checking whether a Mixed Strategy Nash Equilibrium is Evolutionary Stable

Taking the classic Hawk-Dove game I know that there are 3 mixed strategy Nash Equilibria, (H,D), (D,H), and the mixed strategy ((7/12, 5/12), (7/12,5/12)), where those are probabilities of playing H ...
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Nash-equilibrium in mixed strategies with arbitrary payoff function

So I came across this question in an old exam from the lecture I'm currently studying for regarding nash-equilibria in mixed strategies, which for the life of me I cannot seem to be able to find an ...
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How are all kinds of equilibra in game theory connected to each other? (Please correct my summary)

I am a TA in a basic class on game theory in the economics department. I am ashamed to admit, but I do not entirely understand how all the different kinds of equilibria connected to each other. The ...
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Can Pareto Optimality be compared to Nash Equilibrium?

Given a state $s$, and a value function $v^i$ that determines the expected payoff for the i-th agent in that state, can the two definitions below, one of Nash equilibrium and another of Pareto ...
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What is the format of a mixed strategy nash equilibrium?

Take this game where player 1 has choices T and B, while player 2 has choices L and R. We need to find the Mixed Strategy Nash Equilibria. As a side note, it seems like (B,L), and (T,R) are Pure ...
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Find the threshold strategy of a game with incomplete information

I have a question on how to find the equilibrium outcomes of the following game as a function of $(\epsilon_1, \epsilon_2)$. The game There are 2 players. Let $Y_i$ denote the action of player $i$...
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Nash equilibrium in second price sealed-bid auction

I'm trying to understand the basics of game theory and the topic of auctions has arisen. I understand the basic concepts of auctions but I'm struggling with second price sealed-bid auctions. I ...
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Proving that the Wardrop/Nash equilibirum flow on a graph is “stable”?

Let $[0, 1] \subset \mathbb{R}$ be denoted $\mathbb{R}_{[0, 1]}$. Let $[0, \infty) \subset \mathbb{R}$ be denoted $\mathbb{R}_{\geq 0}$. Let $G$ be a finite, connected graph. Associate with each edge ...
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How to find Nash equilibrium in pure and mixed strategies? Problem.

A two player game. Players choose a number from a segment $[0;1]$. A payoff function of the first player $f_1(x,y)=|x-y|,$ where $x$ and $y$ - the numbers chosen by the first and the second players ...
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game theory-Are second priced bids always a nash equilibrium?

I'm trying to understand the basics of game theory and the topic of auctions have come up. What I want to know is second priced bids always a nash equilibrium? Suppose we have this question. We ...