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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Mark vs Zuck game theory [closed]

Mark and Zuck share an apartment. They have different views on cleanliness and, hence, on whether or not they would be willing to put in the hours of work necessary to clean the apartment. Suppose ...
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What is the significance of the findings in Nagel's 1995 paper on Learning Theory?

This post concerns the findings in Nagel (1995). It is a bit outdated but nevertheless still relevant. She examines the Guessing Game, and how individual study-subjects behave in repeated games. In ...
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symmetry of equilibria with heterogeneous players

I have a question about game theory terminology. I am working on a model in which players are heterogeneous in two dimensions, and there are four types of players. For example one type of players ...
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Why is this a zero sum game?

The game is described as follows : In a simplified version of the game Morra each of the players shows one finger or two fingers, and simultaneously guesses how many fingerss the other player will ...
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Sustainability of Collusion in a finite Bertrand competition with N > 2 firms

In a infinitely repeated Bertrand competition, collusion is sustainable if, and only, if, the following inequality is satisfied, $\frac{\pi}{N(1-\delta)}\geq\pi$ Where $\pi$ is equilibrium profits, ...
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Payoff from an option contract

In period 1 the consumer of type $\theta$ selects an option contract consisting of an up-front fee, $B>0$, and exercise price, $\bar{R}$. The consumer pays $B$ at the end of the first period. In ...
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Finitely repeated Prisoner’s Dilemma with switching cost

I'm doing this finitely repeated Prisoner's dilemma with switching costs but I have trouble showing the fact that $\varepsilon$ had to be $1 < \varepsilon < 2$. I do see why and that it is a ...
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146 views

Infinitely repeated game with stationary and symmetric equilibrium

We have two players playing a repeated game. At every period, each player decides to stay or to quit. If both decide to stay, then they both receive 1. If either decides to quit, then the quitter ...
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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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What does 'continuation' as in continuation games, strategies, plays, etc. exactly mean?

I am in my first course in grad level game theory. While I was reading through Fudenberg and Tirole's Game Theory, I constantly come into contact with the word 'continuation' to describe some games ...
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Can perfect behavior be proved in a game of incomplete information?

Assumption: We have a machine that plays games perfectly. The machine plays a game of Chess. Chess is a game of perfect information and complete information. We (assuming we have enough computational ...
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How many Nash equilibria are there in the above game?

5 people are eyewitnesses to a criminal incident. Each one of them wants the police to get informed but they prefer a third person to give the information. Suppose k is one of the 5 people. If the ...
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Game with an equilibrium in pure, but none in mixed strategies?

I came across the following game: The question is to find potential equilibria in mixed and pure strategies. The solution says that there is an equilibrium in pure strategies (B,N), but none in mixed ...
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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....
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Is it worth betting on this case?

Let's imagine a coin-flip game, which uses an unbiased coin. Starting with X dollars, your total increases 50% every time you flip heads. But if the coin lands on tails, you lose 40% of your total. ...
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Set of rationalizable strategies for this 4 x 4 matrix

I would like to find the set of rationalizable strategies for this 4x4 game: The first thing I did was try and find all PSNE. I found two, the ones I bolded. Thus, my answer to this question is that ...
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Mixed Strategy Nash Equilibrium for this particular 3x3 matrix

Suppose I am given the following matrix: I would like to find all MSNE I started by doing the double underline method to find any PSNE. I discovered that none exist. I then looked at which strategies ...
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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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Finding pure-strategy subgame-perfect Nash equilibria

I'm interested in finding the pure-strategy subgame-perfect Nash equilibria of the game below. What is confusing me is that after player A chooses between reducing and not reducing his end payoffs, ...
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Whats the name of the famous hostile takeover where the winner payed less than the loser

In my studies I learned about a bid war ending in a hostile takeover where the winner ended up paying less than the loser offered. It is a very nice demonstration of elements of game theory so I would ...
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The college admissions problem with externalities

In the classic College Admissions problem, there are $m$ colleges and $n$ students. The colleges have a preference over the students and the students have preferences over the colleges. The students ...
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Set of “rationalizable actions”

What does it mean if a question asks me to find the set of "rationalizable actions" for a given game?
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Question regarding preferences in Gale and Shapley (1962)

Is it correct to say that preferences in the classic Gale and Shapley College Admissions problem are quasi-linear? Or is this something thats introduced later in the literature, vis a vis Shapley and ...
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The core and competitive equilibrium

Can someone please explain why the concept of a core is equivalent to a competitive equilibrium? I am just writing a term paper for my matching theory class and I'm having a hard time following along ...
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If a rational preference relation over simple lotteries $\succsim$ are convex then they satisfy independence?

Let´s say there is an uncertain situation with $N$ possible consequences $C = \{C_1, . . . C_N\}$. Assume that there is a rational preference relation $\succsim$ over simple lotteries. I know that if ...
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Exchange Houses game - Bayesian Game

Can anyone help me understand how to solve this type of asymmetric information Bayesian game? So the game is a different version of the Tadelis 'trading house games'. It involves 2 players that each ...
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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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Question about mixed strategy game theory

I have no idea how the game is solved. Especially how do you begin with writing the norm form of the game. Appreciate your help! I assume the probability p of defense playing Left For the opponent's ...
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Gamification and incentives

Is there any (theoretical?) work on "gamification" in game theory? I do not have a proper definition of gamification, but StackExchange would be an example. Contributers like us provide a ...
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SPNE of a normal form game

If we have a sequential game which is equivalent to a simultaneous move game because of its information structure, then the NE we find are also SPNE?
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Finitely repeated prisoner's dilemma without sub-game perfection

Suppose that two individuals play the prisoner's dilemma (PD) a finite number of times; and assume that they both discount the future at a constant rate. Can cooperation be sustained by a Nash ...
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Finding Nash Equilibrium

Where would the Nash equilibrium lie in the pictured scenario? Whats confusing me is that both persons best response changes depending on the choice of the other person (there is no dominant strategy)....
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Parameter in normal form NE

$$\begin{aligned} &\begin{array}{|c|c|c|c|} \hline \text{Player 1 / 2}& x & y & z \\ \hline X & a, a & a, 0 & a, 0 \\ \hline Y & 0, a & 3,0 & 0,3 \\ \hline Z &...
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Dominate strategies in Hotelling

Considering Hotelling's model of linear city and two vendors, we know that by IESDS we end up having that the solution to the game is the midpoint for both vendors yet if we just consider dominated ...
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Rationalizabilitiy and Strict Dominance

When is the set of rationalizable strategies not equal to the set that is left after IESDS? My thoughts are: I know that a rationalizable strategy is that which is a best response for Player i given ...
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Determining subgame perfect Nash equilibriums

Question Three houses share exclusive access to a beach, but it is dirty due to trash washed ashore. A beach clean-up exercise costs $100$, but has a value of $200$ to each household. A clean-up ...
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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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Weak and strict dominance

Im just seeking for confirmation, is it OK to say that : "A strictly dominant strategy is a weakly dominant strategy too"? This would be usefull because for IEWDS we can eliminate strictly ...
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Computing Subgame-Perfect Equilibrium

Suppose that two players play each other for two periods. In the first period they play the first game below, and in the second period they play the second game below. There is no discounting between ...
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Is there a 'fairer' alternative/variant of the White Elephant Gift Exchange?

The White Elephant Gift Exchange is a gift exchanging game that typically has the following rules: Each participant enters one anonymous (ie. wrapped) gift to the pile. There may be rules on what the ...
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What is the point of considering only pure strategies in a game? How could you restrict people from thinking about mixed strategy?

In an experimental setting, how could you effectively incentivize the subjects to not to adopt mixed strategy? I would like to re-emphasize that the question in concern is "how to prevent people ...
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Why utility should be bounded (or unbounded)?

For Expected Utility and SEU, people make axioms to ensure that the utility is bounded. However, I personally believe that the utility function must be unbounded, especially if we are considering ...
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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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One pure Nash equilibrium, no mixed equilibrium?

I'm given a 4x4 payoff matrix \begin{bmatrix}(0,7)&(2,5)&(7,0)&(0,1)\\(5,2)&(3,3)&(5,2)&(0,1)\\(7,0)&(2,5)&(0,7)&(0,1)\\(0,0)&(0,-2)&(0,0)&(10,-1)\end{...
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In a game with alternating moves and complete information, the Nash equilibrium cannot be a non-trivial mixed equilibrium?

Where I can find a simple proof for this fact? For example, a trivial bimatrix game with alternating move has the following payoff matrix: \begin{array}{|c|c|c|} \hline & 1 & 2 \\ \hline U &...
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Information Partition and Common Knowledge

Person $A$ has information partition $\{\{1,2\},\{3,4\},\{5,6\}\}$ Person $B$ has information partition $\{\{1\},\{2,3\},\{4,5\},\{6\}\}$ $w=3$ has been realized. I'm confused about what $A$ knows ...
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What additional axiom to GARP do we need to generate a differentiable or smooth utility function

After researching for a while, I find this: https://www.jstor.org/stable/1913607?seq=2#metadata_info_tab_contents They come up with an axiom called SSARP that generates a preference with smooth demand ...
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What is 2nd round of rationalizability for a 1st price auction?

Consider a first-price auction. Suppose that we have $N$ bidders, and they believe that their opponents' values is drawn from a uniform distribution on interval $[0,1]$. Let us eliminate weakly ...
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Mixed Strategies in Bayes Nash Equilibrium (Bayesian Battle of the Sexes). Shouldn't it depend on $p$?

I have a question about calculating mixed strategies in a Bayes Nash Equilibrium in a simple 2-player bimatrix game. To demonstrate the issue, consider ``Bayesian Battle of the Sexes.'' Suppose P1 ...
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Some questions about Kyle's model in Continuous Auctions and Insider Trading (1985)

I was trying to understand Kyle'e Theorem 1 in page $1319$ in Continuous Auctions and Insider Trading in 1985. As we can see by the proof, this factor $\beta=\frac{1}{2\lambda}$ refers to the ...

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