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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Proofs in the Appendix A of Sannikov (2007)

I have a few questions about the proofs in Appendix A of Sannikov (2007), Games with Imperfectly Observable Actions in Continuous Time. In lemma 4, when he shows the Lipschitz continuity of $H_a(w,\...
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Uniform bounds on rate of merging for Bayesian learners

Update. Cross posted at Cross Validated. In a well-known paper, Blackwell & Dubins (1962) show that the posterior probabilities of two Bayesian agents, whose priors agree on events of measure $0$,...
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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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373 views

Dynamic Bertrand competition when players take turns

Consider the following game: There are two players, $i\in\{1,2\}$ Time is discrete and runs to infinity during periods $t=\{1,2,\ldots\}$ At eat point in time, players have a price $p_i(t)\in\mathbb{...
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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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73 views

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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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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216 views

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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59 views

Algorithmic game theory and decentralized exchange of information

An intresting topic that I want to understad has to do with the decentralized exchange of information among a network of agents, however there is not a specific theory to make such a mathematical ...
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59 views

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). ...
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133 views

Signaling in zero-sum games?

The foundation of this question is a bit vague (based on something overheard at a conference) but I'm hoping someone here can provide some clarification. I overheard a conversation between two ...
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61 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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73 views

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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289 views

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^{...
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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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1answer
303 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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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 ...
3
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1answer
98 views

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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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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Behavioral Dictator Game

I am doing a self study on behavioral economics and I am trying to solve behavioral version of the dictator game with following utilities for person 1 and 2. $$ u_1( \sigma_1, \sigma_2 ) = \...
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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 ...
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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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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 ...
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Bayesian update in the beliefs about the signals

Suppose that we have tow states of the world $\omega_1$ and $\omega_2$, where $p(\omega_1)=p(\omega_1)=1/2$ and there are three different signals, $s_H,s_M,s_L$ that are equally likely to occur in ...
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Strategy definition in an extensive form game

How a (pure ) strategy is defined in an extension form game with information sets? I would like to have both an intuitive and a formal definition. Thank you in advance!
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Strange screening game were FS contracts equals optimal contracts

Consider the setting where a principal hires an agent to do a project. Payoff from project is $\pi = \beta e$, where $\beta \in \{1,2\}$ is the degree of the agent's talent and $e \in [0, +\infty]$ is ...
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23 views

Economics behind reverse auctions with occasional non-profiting suppliers

I was curious about the theory behind a reverse auction system where some suppliers act in a non-profit manner, namely, that their consideration of extra-auctions benefits of providing their service ...
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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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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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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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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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Discount factor and deviating from strategy - Game Theory

I have an exercise in Steven Tadelis Game theory Introduction book (10.2) : Grim Trigger: Consider the infinitely repeated game with discount factor $δ < 1$ of the following variant of the Prisoner’...
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Existence of Bayes Nash equilibria in behavioural strategies

Follow up from this question: 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 \...
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42 views

$a\geq 0$, $x\succsim y$ implies $x+a\succsim y+a$ so the preference is linear?

$\succsim$ is a continuous and local non-satiate weak order. $x,y,a$ are vectors in $\mathbb R^n$ We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero. We want to prove (...
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How far must one reason up the belief hierarchy?

In games of imperfect information, one must reason about the belief on the state of nature, the beliefs of other player's beliefs of their beliefs, and so on. This is referred to as the belief ...
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If a mixed strategy is strictly dominated, then there is a strictly dominated pure strategy in its support?

I am looking at the proof of NE survives the iterated removal of strictly dominated strategies (MWG, ex 8.D.2) and in the solution manual, authors say something like if a mixed strategy is strictly ...
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Are there any experiments about financial games with just one player?

I was wondering if there are any experiments of financial games (laboratory games under controlled circumstances like Plott and Sunder's Rational Expectations and the Aggregation of Diverse ...
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446 views

Second order condition for symmetric game

Denote by $i \in \{1, \ldots, n\}$ an economic agent. Let $\mathbf x \in \mathbb R^n$ denote a vector of actions and $x_i \in \mathbf x$ a typical element. Let further $f_i : \mathbb R^n \to \mathbb ...
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Question on a sufficient condition of contractiveness of best reply functions in Vives (1999)

I have trouble in understanding why a sufficient condition that a best reply function is a contraction. The following is a screenshot of Xavier Vives's Oligopoly Pricing: Old Ideas and New Tools from ...
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Bayes Nash Equilibrium in a game with continuous actions

I am attempting to think through a particular type of game with continuous strategies, with Bayes Nash equilibrium as the solution concept. I first describe the game below, followed by questions. ...
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470 views

What is the difference between utility function and characteristic function

I read that normative theories such as social welfare and game theory have as tasks computing the peoples' (average) utility function in the first case, and the characteristic function in cooperative ...
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Empirical Study of Auctions with Limited Data

I have limited real auction data which I am trying to see if I can do any empirical analysis. The data consists of auction type (i.e., forward or reverse), protocol (e.g., Vickrey, Dutch, English, etc....
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Equilibria for multi-round 'Markov' games?

I'm interested in zero-sum symmetric games which have the following form. Each player has a counter which starts at 0. Each turn, a player may choose from a fixed set of actions. A player's counter is ...