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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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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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).
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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^{...
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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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How to solve the Bertrand model when marginal costs are different and not constant?
Find the equilibrium in the Bertrand model with two firms, with total costs given by:
$TC_1(q_1) = \alpha q_{1}^2$
$TC_2(q_2) = \beta q_{2}^2$
Inverse demand is given by
$P = A - Q$,
where $Q = q_1 + ...
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How to model the payoff (or utility function) of the information provider?
After a thorough look in the literature of information design like Bergemann and Morris and Kamenica and Gentzkow I am still not so sure how the utility gain or payoff of the information provider/...
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Forward Induction Procedure
Does a mechanical set of rules or algorithm exist for doing forward induction on a game tree, or is it an "every problem is too unique and requires its own reasoning" type of situation? I ...
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Dynamic Information Provision model setup - It generalizes Dirk Bergemann and Stephen Morris
The following model setup is from the paper Dynamic Information Provision: Rewarding the Past and Guiding the Future by Ian Ball. It generalizes both the ideas of strategic information transmission of ...
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Solution concept in Benabou/Tirole (2006)
In a well known paper, Benabou/Tirole (2006) examine `pro-social' behaviour in an environment in which others draw inferences about one's motives given the map from motives to behaviour in the ...
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Extensive form game with multiple players
I am wondering on how to draw the extensive form with multiple players. Below is an example of the trust game. How would that look if there were two receivers with potentially different payoffs? Note ...
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Are these two definitions of Bayesian Nash Equilibrium equivalent?
Consider a standard game $\Gamma$ with incomplete information. There are $n$ players indexed by $i=1,...,n$.
$S_i\equiv \{s_{i1},...,s_{iJ}\}$ is the set of actions of player $i$. $S\equiv \times_{i=1}...
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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 ...
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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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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 ...
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Geometric interpretation of transfer function in incentive-compatible direct mechanism
Consider a set of players $i = 1,...,N$ who need to allocate some good. Each player $i$ valuates the good $v_i \in [0,1]$, with $v_i \sim f_i$. An individually rational direct mechanism $(p,c)$, with $...
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Can game theoretic concepts be applied to any groups of strategies collectively partitioning the strategy space?
It is clear that players of a game can almost always create trivial variations on strategies without breaking game theoretic conclusions. For example, a player playing Rock Paper Scissors can play ...
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Modelling common incentives and strategic manipulation
There are many situations in the markets when small or larger portions of traders collude and make a strategy manipulation through communication, even they have heterogeneous endowments and ...
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Public/private knowledge in auctions
Consider three firms that engage in a first-price auction. Firm $i$'s payoff when firm $j$ wins the auction is $S_{i,j}$, which is deterministic and publicly known.
The winning firm $i$ has to pay ...
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Is the mixed strategy $\sigma_i^*:S_i\times\Theta\to\Delta(A_i)$ chosen by player $i$ linear?
Suppose that we have a Bayesian game, where
the number of players is $I$ and we refer to the generic player with $i$
$\Theta$ stands for the state of the world, where $\theta\in\Theta$ is the typical ...
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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 ...
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Pre-play, interim-play, intra-play communication games
I have a question that seems easy but I want some clarification. Suppose that we have a communication Bayesian game. The game starts when the players learn their prior infornation and after this they ...
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Repeated Games of Incomplete information set up and questions
The following are from the model of Jérôme Renault (Repeated Games of incomplete infomration).
The preliminaries of the model
Formally, a repeated game with incomplete information is given by the ...
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