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Questions tagged [bayesian-game]

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Social Welfare and Pareto Optimality in a Bayesian Game

In a normal form game with two players, we call a joint strategy $s=(s_1,s_2)$ a Pareto optimal outcome if for no joint strategy $s'$, for all players $i\in\{1,2\}$, we have $$u_i(s')\geq u_i(s)\qquad(...
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Mixed Strategies in Bayesian Games

I am confused about the following statement from Wikipedia: "A mixed strategy is an assignment of a probability to each pure strategy. This allows for a player to randomly select a pure strategy. ...
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Prisoner's dilemma as a Bayesian one-shot game

What happens if we assume that there is incomplete information to the prisoner's dilemma game? For example, suppose we have the following matrix with the utilities $T>R>P>S$ and $2R>S+T$ ...
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35 views

Bayesian game and the set of types

In a finite Bayesian game, in most textbooks, a type of player $i$ is defined as $\theta_i\in\Theta_i$. Little is said about the "nature" of the set of types. For example, could we have a two-element ...
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Help with a computational method in solving expected payoffs for really large Bayesian game

Im looking for some advice on I can solve my game below computationally because by hand it would take forever. $(1)$ $(2)$ $(3)$ $(4)$ $(1)$ is combination of type $[a,c]$ $(2)$ is combination ...
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Bayesian-Nash equilibrium in a first-price auction

In a famous textbook example of a Bayesian-Nash equilibrium, there is a first-price auction with two independent players. Each player $i$ values the item as $v_i$, which is distributed uniformly in $[...
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1answer
111 views

Bayesian Mechanism vs Prior-free Mechanism

I have a double auction mechanism in which the valuations of the agents for the items are drawn from a known random distribution. To be precise, the valuations are the probability of each agent ...
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Why system of beliefs, $\mu(x)$, needed in dynamic incomplete information games

We need to make statements about the sequential rationality of players who are in information sets that are not singletons. In these non-trivial information sets, we need to be able to say something ...
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Odd Principle in Bayesian-Nash Equilibrium derivation

Consider a two bidder auction with bidders $1,2 \in\mathcal{I}$ with independent private values. Players may be a low valuation type player $V_L$ or high valuation type $V_H$ player. Bidders do not ...
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423 views

Game theory with rational and irrational players

Are there game theoretic models where one player is rational and the other is irrational (i.e., plays with behavioral limitations)? The motivation for this question is that behavioral economics has ...
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2answers
148 views

Compute Nash Equilibrium in median voter game

Consider a spatial model in which two candidates A and B compete for office. The policy space ranges from -1 to 1 and each candidate can take one of three positions, -1, 0, and 1 (so that they have ...
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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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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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Imperfect auditing

Faced a task in microeconomics which is rather complicated with probability. The task is as follows: A university has to hire a new assistant professor. The university can offer two kinds of ...
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314 views

Checking incentive compatibility of a mechanism

I was thrilled at seeing an interesting bidding system in an academic institutions. This bidding is for registration of courses. Each student is allocated some points based on her grade point(GPA). So,...
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1answer
345 views

Divinity for Dummies

I understood the general idea of divinity: that it helps to rule out "unreasonable" equilibria. However, can someone explain it in more details with simple examples so that a senior undergrad student ...
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Arguing uniqueness of Bayes-Nash equilibrium in an auction setting

In an auction setting with interdependent values, let $\theta_i$ denote the type of player $i$ and $m_i$ that player's message (a bid, essentially). I have calculated the best response function as: $$...
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315 views

Bayes-Nash equilibrium and correctness of beliefs

Define a Bayesian game as follows: $$G = \left\langle I, \left(A_i,T_i,(p_{t_i})_{t_i \in T_i}, u_i \right)_{i \in I} \right\rangle$$ $I$ is the set of players $A_i$ is the action set for player $i$,...
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What is the difference between Stochastic game and Bayesian game ?

I was studying definitions of Stochastic and Bayesian game and it appears that Stochastic game is a generalized form of Bayesian game. Could anybody please explain the fundamental differences between ...
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Which economic game theory model is most similar to poker?

Propeties the model should have: Well motivated: the game is actually is a plausible model of a real world situation. Maybe with some parameters learnt from data. Complete: it is a complete game ...
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Can repeated bidding in an auction make each player's type common knowledge?

In Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz(2007), there's a hand-waving argument to justify their setting as a game of complete information: we assume that all values are common ...
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2answers
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Bayesian Nash Equilibrium - Mixed Strategies

What's the correct way to solve BNE in mixed strategies? I've found two conflicting methods used. Two players. Player 1 knows which game is being played, player 2 knows the game is chosen with ...
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239 views

A Perfect Bayesian Bargaining problem

Thought I'd post interesting questions that come my way to try and boost activity! A seller and a buyer negotiate over trade of a single indivisible good. The good is either of low quality (in which ...
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1answer
803 views

Take-it-or-leave-it PBE

I've found an interesting question looking at perfect-bayesian-equilibrium. I haven't seen a question where beliefs are not discrete. There is a single potential buyer of an object which has zero ...
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1answer
219 views

Relationship among universal type space, Aumann's semantic knowledge model and Samet's syntactic knowledge model

What's the relationship among universal type space, Aumann's semantic knowledge model and Samet's syntactic knowledge model? Here's my confusion: Regarding universal type space and the model in ...
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683 views

Perfect Bayesian Equilibrium

I've been given a question which I'm struggling with: Take the standard Prisoner's Dilemma game and consider it is played twice. (Players observe the outcome of the first game before playing the ...
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Models for online markets with reputation system

The only relevant model I'm aware of is Liu Qingmin(2011 R.E.S). Is there any other decent models dealing with the mechanism of online markets under reputation system, and perhaps linking to ...
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How this ex ante game induce a uniform distribution for interim stage?

In an article (see here) from the blog leisure of theory class, it is shown, in an interim stage for a Baysian game, we could run into a technical problem that the induced belief space for a player ...