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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 ...
Ignacio Canabal's user avatar
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 ...
GraceLynn87's user avatar
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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) &...
user9487's user avatar
1 vote
1 answer
25 views

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 ...
Jovan Jezdic's user avatar
0 votes
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.
PiVoyager's user avatar
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(...
user9487's user avatar
3 votes
1 answer
24 views

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 &...
user9487's user avatar
1 vote
0 answers
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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 ...
Ignacio Canabal's user avatar
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1 answer
32 views

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 ...
PiVoyager's user avatar
2 votes
1 answer
49 views

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 ...
PiVoyager's user avatar
1 vote
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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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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 ...
Nishka Singh's user avatar
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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. ...
Jordon Lee's user avatar
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1 answer
15 views

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 ...
ZZZ's user avatar
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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. ...
Ludwig Gershwin's user avatar
1 vote
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63 views

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 ...
Ludwig Gershwin's user avatar
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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 ...
dazednconfused's user avatar
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 ...
Beerus's user avatar
  • 505
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 ...
EconIsHard's user avatar
2 votes
1 answer
134 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 ...
CormJack's user avatar
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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, $(D,R)$ ...
Ludwig Gershwin's user avatar
2 votes
0 answers
54 views

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 ...
Nicolas Torres's user avatar
0 votes
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 ...
Derin dur's user avatar
1 vote
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44 views

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 (...
Ludwig Gershwin's user avatar
3 votes
2 answers
74 views

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 \; ...
Riccardo Iorio's user avatar
4 votes
0 answers
49 views

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? ...
dazednconfused's user avatar
0 votes
1 answer
156 views

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 ...
GraceLynn87's user avatar
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1 answer
40 views

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 ...
Oliver Queen's user avatar
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0 answers
24 views

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?
needeconshelp00's user avatar
1 vote
1 answer
75 views

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_{...
user9487's user avatar
0 votes
1 answer
118 views

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},...
user9487's user avatar
1 vote
1 answer
54 views

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 ...
Oliver Queen's user avatar
0 votes
1 answer
57 views

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 ...
Hãru2you's user avatar
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0 answers
59 views

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 ...
SHYAM's user avatar
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1 vote
0 answers
63 views

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 ...
Ludwig Gershwin's user avatar
1 vote
0 answers
48 views

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 ...
Oliver Queen's user avatar
2 votes
1 answer
96 views

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 ...
Yoji Yamamoto's user avatar
0 votes
1 answer
115 views

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 ...
Ludwig Gershwin's user avatar
2 votes
0 answers
46 views

Kuhn’s equivalence theorem in game theory

I consider a game with two players in incomplete information with perfect recall and I would like to prove Kuhn’s theorem stating that for every mixed strategy $\sigma$ there exists a behavior ...
G2MWF's user avatar
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1 vote
2 answers
282 views

What is strategy profile? Is it -a vector list of si or -the cartesian product of Si?

Which one is correct (a) or (b). If one of them is strategy profile then what is the other called. Which is the standard book to follow for such terminology (a) Some textbooks describe strategy ...
Narayana Srikanth Reddy's user avatar
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0 answers
25 views

Partially Sophisticated Quasi-Hyperbolic Discounting Problem

I am trying to follow the bottom method for partially sophisticated hyperbolic discounting... The setup (modified from an earlier problem in the same course) is that a person will get different "...
user10478's user avatar
  • 423
1 vote
0 answers
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Is there any research about mechanism design with more than two choice variables?

In traditional mechanism design problem, there are only two choice variables (regardless the payoff function of agent is quasilinear or not), which makes the strictly increasing difference of payoff ...
Perry_W's user avatar
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Which TV Station Benefits More from Mutual Program Broadcasting: A with More Viewers or B with Fewer?

If there are two television stations, A and B, producing similar programs, and A has many more viewers than B due to they started earlier, then if both stations allow each other to broadcast their ...
hello.wjx's user avatar
  • 101
2 votes
0 answers
67 views

How Kyle's $\lambda$ emerges in the demand functions of the informed and uninformed traders?

From Albert S. Kyle's 1989 model. Suppose that the are trhee types of traders in the market, informed traders (I), uninformed traders (U) and noise traders. The population of $I$ traders is $N$ (...
Oliver Queen's user avatar
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0 answers
47 views

What are the arguments for and against the supremacy of the current self?

In this video, the professor attempts to explain how the course's motivation of temporal discounting makes (what strikes me as) a pretty extravagant assumption. Now, if you think about your future ...
user10478's user avatar
  • 423
1 vote
2 answers
123 views

Unwrapping Kamenica and Gentzkow model

Let's start with the basics. Suppose that $\Theta$ is a finite set of states and $\theta$ is the element of the state set. To simplify the model, we assume that $\Theta = \{\theta_1 = G, \theta_2 = B \...
Oliver Queen's user avatar
2 votes
1 answer
70 views

Beyond quadratic loss preferences?

I have a complex question. Is there any other way to model the preference misalignments of the sendres (in senders-receivers games) towards the desire of some specific state apart from the quadratic ...
Oliver Queen's user avatar
1 vote
1 answer
71 views

(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 ...
Nazarene's user avatar
3 votes
1 answer
69 views

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, $B$ ...
fruitless fruit juice's user avatar
0 votes
1 answer
60 views

Can a Subgame Perfect Equilbrium consist of a weakly dominated action?

I was reviewing the Market Entry game and observed that 'being mean to the entrant' is weakly dominated by 'being nice to the entrant.' Coincidentally, 'being nice to the entrant' is also part of the ...
wes BOREland's user avatar

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