# 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 ...
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### 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 ...
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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) &...
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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 ...
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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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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(... • 89 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 &... • 89 1 vote 0 answers 19 views ### 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 ... 0 votes 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 ... 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 ... 1 vote 0 answers 36 views ### 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 ... • 11 1 vote 0 answers 10 views ### 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 ... 0 votes 0 answers 43 views ### 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. ... 0 votes 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 ... • 25 0 votes 0 answers 26 views ### 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. ... 1 vote 0 answers 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 ... 0 votes 0 answers 14 views ### 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 ... 5 votes 1 answer 95 views ### 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 ... • 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 ... 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 ... • 991 2 votes 0 answers 39 views ### 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 0 answers 55 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 ... • 2,259 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 ... 1 vote 0 answers 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 (... 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 \; ... 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? ... 0 votes 1 answer 158 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 ... 0 votes 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 ... • 370 0 votes 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? 1 vote 1 answer 76 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_{... • 89 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},... • 89 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 ... • 370 0 votes 1 answer 62 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 ... 0 votes 0 answers 61 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 ... 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 ... 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 ... • 370 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 ... 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 ... 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 ... • 121 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 ... 0 votes 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 "... • 423 1 vote 0 answers 31 views ### 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 ... • 111 0 votes 0 answers 10 views ### 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 ... • 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$N$(... • 370 0 votes 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 ... • 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 \...
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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 ...
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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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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, $B$ ...