# 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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### Can I refine the set of equilibria in a signaling game to the sender-optimal outcome?

Main question: I've been reading about communication games a lot, and I'm wondering if there are good criteria to select between two separating-ish equilibria. I think of a separating equilibria as ...
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### How do you strategically vote to put someone in last place?

I watch a dumb reality TV show which has a certain number of contestants to start with, and every week one contestant is eliminated. Here's how the elimination process works. Every week a certain ...
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### In experiments of 2-by-2 games where the dominant action benefits both players, do people frequently choose the other action?

Sayers et al look in Some descriptive aspects of two-person non-zero-sum games at variations of the prisoner dilemma. They had two participants (α and β) pressing press either a black (1) or a red (2) ...
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### How to find an optimal strategy in an auction?

I have asked this question in mathematics forum as well but since I have not recieved an appropriate answer yet, I ask it here as well. Consider an auction of sculptures by four artists: A, B, C and D....
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### Optimal Fight Purse and Boxing Strategies

The following is all public information available to all the players in this scenario. The General Setup In the aftermath of the infamous race between the tortoise and the hare, the salty hare went ...
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### Game with predatory player (reference request)

I am interested in a multiplayer game where one player gains utility, not just by winning, but by seeing one other player (chosen in advance) lose (or come in last place if the game has an ordered ...
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### How do supply chains form?

I am trying to put forth a theory for endogenous supply chain formation. A set of $K$ complementary tasks need to be performed to manufacture a good $G$. If manufactured, there exists a demand ...
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### Perfect Bayesian Equilibium - Application to game with inconsistent beliefs / no common prior

Does the concept of a Perfect Bayesian Equilibrium apply only to incomplete games with a common prior / consistent belief? In both Bonanno's "Game Theory" and Osborne's "A Course in ...
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### Existence of symmetric trembling hand perfect equilibria

Consider symmetric and finite game. By Nash (1950), the game must have at least one symmetric equilibrium (proof). Also, it must have at least one trembling hand perfect equilibrium (proof). ... 64 views

### Unique Nash-equilibria in multi-unit auctions with uncertain participation

Setup Consider a one shot sealed bid multi-unit auction where $N$ bidders compete for $K$ identical objects and each bidder $i$ has demand $d_i\in \{1,\dots,K\}$. Bidders receive private i.i.d. ...
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### Existence of nash equilibria in finite games

I was going through the proof of existence of a Nash Equilibria in finite normal form games (Proof via Brouwer’s theorem) and got a question regarding the requirement of finiteness for the number of ...
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### Why is the symmetric grim trigger not a Nash?

Consider the stage game: Let $\delta\in(0,1)$ be the discount factor. Let $G$ be the symmetric grim trigger strategy profile. The payoffs are then E_{A}(G) = E_{B}(G) = \sum_{i=0}^{\infty}3\delta^{... 466 views

### Papers on Game Theory and the Housing Market

Professor George Fallis in his book "Housing Economics" writes: (Chapter 4 pg. 78) The (home)owners will establish a pricing strategy depending on how they believe demanders are behaving; ...
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### Game With Natural Disruptions

Consider a static game with complete information, where each player makes a decision $a_i$ and receives a payoff $\pi_i(a_i,a_{-i})$. Now suppose there is a natural disaster modeled by a binary random ...
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### Screening models with multiple goods and interacting costs

I'm looking for a reference in the literature on monopolistic screening/mechanism design, where there are multiple allocative variables and these interact in the agent's utility function. For example, ...
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### Extension of Harsanyi Transform for Two-sided Incomplete Information Games to Beliefs with Zero Probability

In the textbook I'm reading "Game Theory - Giacomo Bonanno", one requirement to applying the Harsanyi transform to convert a two-sided incomplete information game to an imperfect information ...
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### Providing an example in cooperative - games and coalitions

Here is the paper from chich I previously posted another definition here Definition of a $k-$strong Nash Equilibrium I am trying to construct an example to understand the idea of the following ...
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### Super and sub modular games

I was trying to read up on super and sub modular games. I have started with basic survey papers like the one by Rabah Amir (2005). Research papers assume a lot of common knowledge (the papers that I ...
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### Gale's version of the Rubinstein-Wolinsky (1985) model

Likely to be a very stupid doubt. I am reading Douglas Gale's book "The Strategic Foundations of General Equilibrium", which presents a brief version of "Equilibrium in a Market with ...
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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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### Perturbing distributional strategies on a measure zero set

In the context of a Bayesian game, $\Gamma = \left< (\Theta_i,\mu_i)_{i \in N}, (A_i)_{i \in N}, (u_i)_{i \in N}\right>$ where type of agent $i$ is drawn from $\Theta_i$ according to a ...
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### Asymmetric Nash Bargaining

The Nash bargaining solution selects the unique solution to the maximization problem $\max_{s_1, s_2 } (s_1 - d_1) (s_2 - d_2)$ such that the solution satisfy the following axioms : Invariance ...
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### Mean Field/Differential Game and Measurability

Consider the following scenario. There is a continuum of players in a population, with population measure normalized to $1$. Each player has a type $\theta \in [0,1]$ and we suppose that $\theta$ is ... 89 views

### Insurance question: need a brief explanation

Two risk averse people are identical in every way (including wealth, W , amount of loss, L, and utility function, U(W)) except they have different probabilities of loss. Suppose they want to buy ...
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### Terminology and formalization for "anonymous" game forms

I have an intuitive notion of what an "anonymous" (extensive) game form $\Gamma$ is. In my mind an "anonymous" game is a game in which the players' identity does not matter. This includes the (again ...
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### AIC Calculation

Our object is calculating AIC, and we are unsure whether we can use our measure below when calculating AIC. The following are the data from the experiments and our method to calculate the information ...
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### How much information is required to manipulate a mechanism?

It is well-known that the first-price auction is manipulable, in that a player can improve his utility by bidding less than his true value. But successful manipulation requires information: the player ...
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### question about lemma 1 of Crawford & Sobel (1982)

In Crawford & Sobel (1982), they proved in lemma 1 that for the basic model of a cheap talk game, every equilibrium induces finitely many actions. Here is a special case of their model where the ...
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### Two questions in Bergemann and Morris (2016) - BCE and Comparison of Information Structures in games

Based on Begemann and Morris (2016) we have the following definition about a standard game of incomplete information A standard game $\Gamma = <G,S>$ of incomplete information consists of a set ...
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### Subgames in imperfect information games

I have not previously come across three player games and I am trying to solve for the subgame perfect NE/equilibria for the following game, where player 3's decision node is linked to the decisions of ...
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### Every Submodular Valuation Can Be Represented as a Maximum of Additive Valuations

According to this paper, "every submodular function can be represented as a maximum of additive valuations." It gives an algebraic description as well, but I am having trouble internalizing ...
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### Expected utility maximization question

If the utility function of an individual is $u(w) = 10 \sqrt{w}$ and the individual starts with $w = 100$ (where $w$ denotes the wealth available to him). If he buys a lottery that costs him $51$ and ... 17 views

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### Job Market Signaling w/Continuous Ability

I am currently trying to brush up on job signaling models for the upcoming semester, and came across this old exam question. There are no solutions to the question (that I am aware of), and I'm having ...
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### Is Glicksberg's existence theorem a generalization of Nash Existence Theorem?

I am now learning Game Theory by Fudenberg and Tirole, and I am thinking whether Glicksberg's existence theorem is a generalization of Nash Existence Theorem. Theorem 1.1 in FT (Nash): Every finite ...