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Questions tagged [game-theory]

Game theory is a study of situations of strategic interaction between two or more players in which there is a predefined set of rules and an outcome associated with each choice taken.

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What kind of figures are insightful in game theory?

I am finishing my thesis on a signalling model in which I characterize the perfect bayesian equilibria of the game. However, I find that my final expressions are too mathematical and that the ...
1 vote
2 answers
63 views

Mixed Strategy Nash Equilibirum, Contributing to a Public Good

I'm a economics undergrad student currently studying the basics of Game Theory. I'm trying to solve the following mixed strategy game: -Two players, Player 1 and Player 2 -Available actions: Each ...
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2 answers
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Why is the number of subgames in these two games different?

This game has only 1 subgame (the game itself). This game has 3 subgames. Why is it different? I don't know how to judge the number of subgames.
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2 answers
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Nash Equillibrium - Depend On The Opponent's Strategy?

Say I have the following pay-off matrix: For a one-shot game, it is easy to see, that (low, low) is the only Nash Equillibrium in the payoff-matrix. However, say we're playing an infinitely repeated ...
2 votes
2 answers
135 views

Finding the subgame-perfect equilibrium in sequential games with infinite action spaces

Firms 1 and 2 are competing in the same market. Each firm $i$ must choose a quantity $q_{i}$ to supply, and the market price $p$ will depend on their choices according to the inverse demand formula $p(...
3 votes
2 answers
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State space of the vector of strategies in evolutionary games

I'm reading Evolutionary Game Theory by Jason MacKenzie Alexander, and the author, whilst introducing the dynamical-systems treatment of evolutionary games, defines the vector $\vec{p(t)} = \langle \; ...
2 votes
2 answers
234 views

All-pay auction question problem

In a sealed bid all pay auction, the highest bidder receives the good but every buyer pays the seller the amount of her bid regardless of whether she wins. Suppose there are two bidders whose ...
1 vote
1 answer
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Finding the mixed-strategy Nash equilibrium in this game

Find the pure and mixed-strategy Nash equilibrium in this game: \begin{array}{c|cccc} P_1 \text{/} P_2 & \text{Ll} & \text{Lr} & \text{Rl} & \text{Rr} \\ \hline \text{T} & (3,2) &...
9 votes
2 answers
331 views

Gale-Shapley Follow-up Literature and General Questions

The Gale-Shapley Algorithm is a way of matchmaking between two different entities of people. It guarantees that every individual player is matched and that the matches are stable. What sort of ...
1 vote
1 answer
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Can a mixed strategy that is strictly dominant exist if there is no strictly dominant pure strategy?

Consider a simultaneous-move game with two players, 1 and 2. Player 1 does not have any pure strategy that is a strictly dominant strategy. Is it possible for player 1 to have a mixed strategy that is ...
3 votes
1 answer
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Finding the normal representation of extensive form game

Consider a game where player 1 must choose T or B, player 2 must choose L or R, and their payoffs depend on their choices as follows. $$ \begin{array}{c|cc} \text{P1} \backslash \text{P2} & L &...
2 votes
1 answer
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How to judge whether NE involves a Weakly Dominated Strategy?

Consider the following normal form game: (i) Find all Nash Equilibria in pure strategies. I know how to find it. The answer is $\mathrm{NE}:\{C ; Y\},\{D ; Z\}$. (ii) Based on the Pareto Dominance ...
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Exponential utility with distance to the average carbon emissions of the industry

I am writing a thesis on sustainable finance and I am considering a game where the 2 players are firms wishing to maximize firm value through an investment in green technology to reduce carbon ...
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2 answers
109 views

bertrand duopoly with discrete price

There is a 2 firm, engaging in price competition. Total costs are CA(q)=10q and CB(q)=21q and the inverse demand is P(q)=120-q What is the equilibrium profits? What is the maximum amount that firm A ...
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1 answer
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How many subgames are there in this game?

Consider the following extensive form game: How many subgames are there in this game? Suggested Solution: There are two subgames. One after P1 plays R and P2 plays r, and then the whole game. My ...
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Alternating offer bargaining game with probability

Consider a variant of the alternative offers bargaining game. Two players are bargaining over the split of a pie of total size/value 1; each player likes as big a share as he can get. In each round, a ...
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Game theory one shot deviation principle

Consider a variant of the alternative offers bargaining game studied in class. Two players are bargaining over the split of a pie of total size/value 1; each player likes as big a share as he can get. ...
1 vote
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sequential game with stackelberg duopoly

Two firms, A and B, compete in a market selling identical goods. The market demand curve is given by Q = 100 − P. Firms set prices PA and PB. A chooses its price first, then observing it, B chooses ...
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1 answer
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Market signaling with a national exam

Question: Consider an economy with a competitive labour market in which firms pay a wage equal to the expected productivity of the employee. There are two types of employees: Good (with a productivity ...
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How to find mixed-strategy nash equilibrium payoff in this game?

Suppose there are 2 players. Each player chooses a non-negative integer $(0,1,2,\cdots)$. The players make their choices sequentially, with the second player observing the choice of the first player. ...
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1 answer
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public good contribution game theory

Public Good Contribution: Three players live in a town, and each can choose to contribute to fund a streetlamp. The value of having the streetlamp is 3 for each player, and the value of not having it ...
5 votes
1 answer
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About Two Methods of Computing Bayesian Equilibria

Question I want to compute the Bayesian equilibria for the following Bayesian game: With probability $p$, player 1 would be of type 1.1. With probability $1-p$, player 1 would be of type 1.2. Player ...
1 vote
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How do I show that if there are more than 2 types in a signaling game, then multiple equilibria satisfy the intuitive criterion?

I'm trying to figure out why in a signaling game with more than 2 types, multiple equilibria with different equilibrium strategies satisfy the intuitive criterion. Take the classic Spence job market ...
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Papers on signalling + validation?

Looking to see if there's any game theory literature in which 2+ players play a game of incomplete information. One set of (informed) players gives Spence-like signals to the uninformed player(s). The ...
2 votes
1 answer
135 views

Zero-Sum Game with two Mixed Equilibrium Interpretation

In the attached Zero Sum Game, i have solved for two Mixed Nash Equilibrium, $(l,m)$ and $(m,r.)$ In $(l,m)$ the payoff is $8/5$ to $P_1$, and $-8/5$ to $P_2$. Here $P_1$ mixes between Top and ...
1 vote
1 answer
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Find the Pure Nash Equilibria in this Two-Player Strategic Game

Players 1 and 2 are involved in a joint project. Each player i independently chooses an effort $c_{i}$ that can be any number in the interval from 0 to 1; that is, $0 \leq c_{1} \leq 1$ and $0 \leq c_{...
2 votes
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Help me understand Harsanyi's purification theorem

I'm trying to find a game that cannot be purified. Here's an examle from Game Theory by Fudenberg & Tirole: Consider a $2\times 2$ game: There are 2 PSNE: $(U,L)\;\&\;(D,R)$. However, $(D,R)$ ...
2 votes
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Are there Sequential Equilibria that are not Trembling Hand Perfect Equilibria, that don't involve Weakly Dominated strategies?

I'm taking an advanced course (graduate level) in Game Theory. My class has covered several equilibrium concepts, up to Sequential Equilibrium. The professor said that there are already more ...
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1 answer
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Can There Be a Dominant Strategy If Both Firms Choose to Match the Lowest Price in the Market in a Bertrand Model of Competition?

In a Bertrand duopoly model where firms choose to price match ie match the lowest price in the market, any price p∈[c,Pm] (where c is cost and Pm is the monopoly price) can be a Nash. Hence, there are ...
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1 answer
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How to find BNE of the exchange game?

Each of two players receives a ticket t on which there is a number in [0,1]. The number on a players ticket is the size of a prize that he may receive. The two prizes are identically and independently ...
1 vote
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Why is there no subgame perfect equilibrium in a sequential two-player first-price auction?

Consider a two-player first-price auction with complete information, in which players' values $V_2\geq V_1$ for the prize are commonly known. If the players tie, the winner is determined randomly (...
4 votes
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Game where you don't know (but can learn) your own type?

Is there a literature out there for games where you don't know your own type, but know it's from a distribution, and can e.g., invest resources to learn your own type prior to moving on with the game? ...
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1 answer
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On and off equilibrium path game theory

I am super confused about on and off equilibrium path equilibria. Is it safe to say Nash equilibria can be on or off the equilibrium path due to the fact that one player could be irrational and ...
2 votes
1 answer
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Can game theoretic concepts be applied to any groups of strategies collectively partitioning the strategy space?

It is clear that players of a game can almost always create trivial variations on strategies without breaking game theoretic conclusions. For example, a player playing Rock Paper Scissors can play ...
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1 answer
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Two candidate voting game on the unit interval ideological spectrum (game theory exercise)

(Politics game) Consider a population of voters uniformly distributed along the ideological spectrum from left $(x = 0)$ to right $(x = 1)$. Each of the candidates for a single office simultaneously ...
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Sequential Bertrand competition Nash equilibrium when marginal costs are zero

How do I find the Nash equilibrium in sequential Bertrand competition between 2 firms if both their marginal costs are zero?
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1 answer
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Find the Nash Equilibria in this Two-Player Strategic Game

Find the non-randomized Nash Equilibria of this two-player strategic game, in which each player's set of actions is the non-negative real numbers, and the players' payoff functions are: $$u_{1} (c_{1},...
3 votes
1 answer
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Why does the voter paradox entail 0 turnout?

The decision to cast a vote (under a simplistic FPTP two-candidate model), as formalised by Downs can be written as follows: $pB \geq C$ where $p$ is the probability of you changing the outcome, $B$ ...
1 vote
1 answer
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Judge prosecutor example of Kameinica and Gentzkow

Based on Kamenica and Gentzkow example about the prosecutor and the judge. The utilities of the sender and the receiver are $v(\alpha,\omega)=\alpha$ and $u(\alpha,\omega)=-(\alpha-\omega)^2$. The ...
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Bertrand Duopoly game

Consider the Bertrand’s Duopoly game with demand D(p) = α − p. Assume that each firm is restricted to choose a price is an integer. Also, assume that each firm has a constant marginal cost c is an ...
9 votes
3 answers
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How infinite Nash equilibria are possible in a game?

I was studying games when one of the players seems to be indifferent between two or more pure strategies because he gets the same payoff with each strategy. We say that there are infinite Nash ...
1 vote
1 answer
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Can anyone help with these calculations?

This is from the this paper in section $3$ about the two period example. Suppose that we have the following two period, $t=1,2$, sender(S) - receiver(R) model. For an action path $a=(a_1,a_2)$ and a ...
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1 answer
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Expected number of players buying a product

There is a continuum of players who want to buy a product. The utility to each player from that product is $q$. If he does not buy the product, his utility is zero. The random variable, $q$, has a ...
1 vote
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How do I solve for the Nash equilibria in the Hotelling price competition model

I'm trying to find the Nash equilibria in the following problem: Two firms produce an identical product with no fixed costs. The marginal cost of each firm $i=1,2$ is $c_i\in (0,1)$. Customers are ...
1 vote
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Why did Bergemann and Morris chose a different setting with respect to Kamenica and Gentzkow only to reach to the same results?

Why did Bergemann and Morris choose a different setting with respect to Kamenica and Gentzkow only to reach to the same results? However none of both approaches seem to present the problem in a ...
2 votes
2 answers
227 views

Mechanism design making the Government reveil its indiferrence price towards goods

In order to Tax non-monetary property and wealth the government sets an arbitrary price (they are not even personalized assesments) and often people transact below that price. I have bought and sold ...
1 vote
2 answers
142 views

Multi dimensional Auction in economics

I am following this paper . They have different suppliers and one buyer and They are using auction to select best suppliers Suppliers will submit. suppliers offer a multidimensional bidding on quality ...
2 votes
1 answer
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Differences of two discount factors

In game theory at the undergraduate level, the discount factor is denoted as $\delta \in [0,1]$. On the other hand, in macroeconomics at the graduate level, the notation $e^{-\rho t}$ is used($t$ is ...
1 vote
1 answer
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(Mechanism Design | Mailath Exercise 10.5.3) A Question

Hi, everyone! I'd appreciate some help with this problem, please. Suppose that a seller puts a one-unit good on the market, and a buyer comes around with an unknown valuation $θ$. This buyer has a ...
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1 answer
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Trying to understand the relationship between the normal form and the extensive form

I'm trying to prove the following statement: Prove that if in a 2X2 normal-form game all payoff vectors are distinct, then up to relabeling of actions the game has exactly two extensive forms in ...

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