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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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When action and strategy differ in game theory

It looks like in a static, simultaneous move game, action is used interchangeably with strategy. But when do they differ, say in a more complicated game structure? I am trying to understand the ...
Frank Swanton's user avatar
9 votes
2 answers
11k views

Imperfect vs incomplete information

What's the difference? To illustrate, please give examples of A game with perfect but incomplete information; and A game with complete but imperfect information. Related.
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9 votes
2 answers
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Meaning of Additively Separable, Linear in X

Often I see both in micro and macro two common terminology : Additively separable. Linear in price or linear in probability. I understand exactly as they sound by looking at the functional form ...
Frank Swanton's user avatar
1 vote
0 answers
153 views

Please check for payoffs which I calculated in the incomplete and imperfect game

Taxpayers may either have a high income or low income, and they may be either opportunistic or honest. The tax collector cannot observe any of these characteristics, but after receiving a report from ...
studentp's user avatar
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31 votes
3 answers
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How to intuitively understand the 'Intuitive criterion'?

The intuitive criterion by Cho and Kreps is a refinement to minimise the set of perfect Bayesian equilibria in signalling games. What would a simple and intuitive example to explain this criterion be? ...
Bravo's user avatar
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8 votes
4 answers
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Nash equilibrium of a Bertrand game with different marginal costs

Consider the following game of Bertrand (price competition): There are two players, $1$ and $2$. Each has a publicly known marginal cost, $c_i$. A strategy is a price, $p_i\in\mathbb{R}$. Player $i$'...
Ubiquitous's user avatar
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5 votes
2 answers
501 views

Are direct mechanisms always truthful?

I am very new to mechanism design so I am a bit lost among the concepts, even the most basic ones. One thing that is not clear to me is the concept of direct mechanism and its relationship with the ...
PhDing's user avatar
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Bertrand game - Nash equilibrium

The quantity is limited to 300 but the monopoly quantity is equal to 400 and gives a monopoly price of 600. But if we plug the quantity of 300 into the demand function we get a price of 700.But I am ...
Stefanos Makridis's user avatar
4 votes
2 answers
333 views

Finding PBE in incomplete game

Taxpayers may either have a high income or low income, and they may be either opportunistic or honest. The tax collector cannot observe any of these characteristics, but after receiving a report from ...
studentp's user avatar
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3 votes
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Oddness of equilibrium points

I have seen that generically any finite games have odd number of equilibria. So for $2\times 2$ games can we say that generically they must have $3$ equilibria? If not can you give an example of games ...
user64066's user avatar
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Why are second price auctions preferred if they don't maximize expected revenue?

The reasoning usually given for why you would use a second price auction (SPA) as opposed to a first price auction (FPA) is that FPA encourage underbidding while SPA encourage truthful bidding. That ...
Steve's user avatar
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Can a dominance solvable game have a mixed strategy equilibrium?

Prelude: we get this question about specific finite games. Let us answer it generally. (examples 1, 2) Suppose there is a two-player finite game (a "matrix game") where both players ...
Giskard's user avatar
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3 votes
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Identifying Nash equilibria in extensive form game

Is there a systematic way of identifying all (pure strategy) Nash equilibria (not just the subgame perfect ones) in an extensive form game? In the following Entrant v Resident example, there are three ...
Herr K.'s user avatar
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3 votes
2 answers
765 views

Subgame Perfect Nash equilibrium: two stage game

Charitable organizations are ranked according to the proportion of their total budget that is spend on programs(what directly goes to the recipients of their services) relative to money spent on ...
Stefanos Makridis's user avatar
3 votes
1 answer
2k views

Maxmin and minmax strategies

I was solving for a stable equilibrium in the following 2 player zero sum game. I need to calculate the equilibrium using maxmin and minmax strategies. In this game they should come out to be ...
Sub-Optimal's user avatar
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2 votes
1 answer
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Signalling Game, Multiple Signals

I am solving a three-stage game in a supply chain with one buyer and one supplier. The supplier has private information on its production capacity. The supplier also has the option to sell to the ...
user3425989's user avatar
0 votes
1 answer
455 views

Question on oligopoly.

Consider an oligopoly between two identical firms producing a homogenous good with constant marginal cost where firms face linear market demand. $B_i(q_j)$ denotes firm i’s best response given the ...
studentp's user avatar
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17 votes
5 answers
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Visualization tools for game theory: Decision trees

There are many ways to draw a sequential game 'by hand'. By drawing the game I mean this: Displaying players' decision points, available actions and payoffs. Is there any way I can do this in R or a ...
Giskard's user avatar
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Osborne, Nash equilibria and the correctness of beliefs

In Osborne's An Introduction to Game Theory Nash equilibrium is described as follows (p. 21–22): First, each player chooses her action according to the model of rational choice, given her beliefs ...
Jyotirmoy Bhattacharya's user avatar
14 votes
2 answers
2k views

Rosen's Diagonal Strict Concavity condition

Consider a game with $n$ players, with strategy space $S \subset \mathbb{R}$, where $S$ is bounded set, and player's $i$ payoff function $\pi_i:S^n \rightarrow \mathbb{R}$. Rosen's condition (J. B. ...
Nidjsi's user avatar
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11 votes
1 answer
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How does Google price the items on Google Play?

I am a fledgling computer science researcher working in intersection of economics and computation. Please excuse me if this question seems out of place to the administrator. I am currently studying ...
pareshnakhe's user avatar
9 votes
3 answers
6k views

How infinite Nash equilibria are possible in a game?

I was studying games when one of the players seems to be indifferent between two or more pure strategies because he gets the same payoff with each strategy. We say that there are infinite Nash ...
Sub-Optimal's user avatar
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8 votes
2 answers
389 views

How to auction shared item with a roommate?

My roommate and I split the cost of a game console a year ago (~$400) but he is now moving out. We were wondering how to fairly auction the console given the situation: We both paid an equal price ...
ma22's user avatar
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7 votes
2 answers
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What determines the outcome of a price war, and why isn't that outcome reached instantaneously?

Mary is making a hefty profit manufacturing and selling widgets. Jim has some money laying around and he is trying to figure out if he shouldn't start manufacturing some widgets too. In this example ...
ZKe's user avatar
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0 answers
406 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{...
Ubiquitous's user avatar
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7 votes
2 answers
3k views

Asymmetric vs incomplete information

I am having difficulties in distinguish them. I kind of understand what is the difference intuitively, but I still fail to put some games in the correct category. Can you give me two examples of ...
Lex's user avatar
  • 235
7 votes
1 answer
255 views

Convex hull operator in the definition of rationalizable strategies

In Game Theory by Fudenberg and Tirole, they define the set of rationalizable strategies in the following way. Definition 2.3 in FT: Set $\tilde{\Sigma}_{i}^{0}=\Sigma_{i}$ where $\Sigma_{i}$ is the ...
John's user avatar
  • 357
6 votes
1 answer
278 views

Bayes Correlated Equilibrium: obedience

I would like your help to understand the definition of obedience in an incomplete information game at p.7 of this paper. Let me summarise the definition provided in the paper. There are $N\in \...
Star's user avatar
  • 446
6 votes
1 answer
251 views

Mechanisms to incentivise social welfare

Suppose there is a set of agents causing loss $l_i$ to themselves and aggregate loss $L$ to the society, both of which can be minimised by their investments $c_i$. The social planner who is concerned ...
Bravo's user avatar
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6 votes
1 answer
160 views

Are symmetric equilibria continuous with respect to the payoff matrix?

Assume a two player symmetric game where the payoff for the row player is given by: $$ A = \left( \begin{array}{cc} a_{1,1} & a_{1,2} &\cdots & a_{1,n}\\ a_{2,1} & a_{2,2} &\cdots &...
R B's user avatar
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6 votes
1 answer
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Difference between Sequential and Weak Sequential (Weak Perfect Bayesian) Equilibria?

This is in reference to the Game theoretic concepts as Nash equilibrium refinements. Sequential equilibrium are often defined as satisfying two conditions: consistency and sequential rationality. ...
user6733's user avatar
5 votes
1 answer
412 views

Axiomatic Bargaining: Kalai-Smorodinsky and Nash solutions coincide

Under standard assumptions on the domain of bargaining problems like Pareto Optimality, Symmetric, Scale Invariance and Independent of Irrelevant Alternatives / Individual Monotonicty, in which ...
John Stern's user avatar
5 votes
1 answer
2k views

Example of a game with no Nash equilibria but at least one correlated equilibrium

In this answer there is the offhand remark Of course, a game with no Nash equilibria may have a correlated equilibrium, but I'm not aware of any simple examples where this is the case. Can ...
Giskard's user avatar
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5 votes
1 answer
844 views

Definition of Bayesian Nash equilibrium

I have a basic doubt on the definition of Bayesian Nash equilibrium. Consider the following game: 1) $N$ players. 2) Each player $i$ has a type, assigned by nature and denoted by $\epsilon_i$. ...
Star's user avatar
  • 446
5 votes
2 answers
430 views

Define and characterize equilibria of the following game

Consider the following game between a monopolist firm and a consumer. Consumer's income is $1$, and he needs to allocate it between period 1 and period 2 consumption to maximize his utility $u(c_1,c_2)...
night_owl89's user avatar
5 votes
1 answer
130 views

How game theoretic models and analysis is different from ABM?

"An agent-based model (ABM) is one of a class of computational models for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or ...
ykn's user avatar
  • 51
4 votes
1 answer
7k views

Cournot Competition game with 3 Firms

Three firms are in Cournot competition. The inverse demand curve is denoted p(q) where p is the price if a total of q units are produced. Assumptions are: p(0)>0 and p'(q)<0 and p''(q) $\le 0$ ...
Stefanos Makridis's user avatar
4 votes
1 answer
14k views

Mixed strategy Nash equilibrium in 3x3 game

What is the MSNE for the following game? I think you can eliminate strategies $A$ for player 1 and $C$ for player $2$, as these will are weakly dominated by all other strategies. Then, the game ...
Пафну́тий's user avatar
4 votes
1 answer
166 views

Difficulty in understanding the notation related from probability theory with game theory

The question that I have is a little technical and it has to do with the notation and the combination between some mathamatical properties in the probability theory of information economics. Say $\...
Nav89's user avatar
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4 votes
1 answer
181 views

The notions of Bayes Correlated Equilibrium and Bayesian Nash Equilibrium in a game with one player

I would like your help to use the correct terminology to define a Bayes Correlated Equilibrium (BCE) and a Bayesian Nash Equilibrium (BNE) in a "game" with one player. The notion of BCE in an $N$-...
Star's user avatar
  • 446
4 votes
1 answer
333 views

Bounded rationality with Quantal Response Equilibrium model for an Extensive Form game

I am working on my Master thesis based on bounded rationality in behavioral game theory models, I wanted to know if QRE(Quantal Response Equilibrium) can be applied to games where players have ...
Amogha Varsha's user avatar
3 votes
2 answers
90 views

Exact definition of one-player Bayesian Correlated Equilibrium

Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world $V$. The state of the world has support $\mathcal{V}$. ...
Star's user avatar
  • 446
3 votes
2 answers
3k views

Game theory - Definition problem - Strategy vs Action

A one definition is given by : Strategy is one of the possible actions of a player But I'm having a trouble. When working with games, We specify a strategy set $S$ and a strategy $s \epsilon S$. ...
Kuantew's user avatar
  • 281
3 votes
2 answers
603 views

Correlated Equilibrium for Rock Paper Scissors

Consider the game of Rock, Paper, Scissors (RPS), with payoffs given as follows: Is there a correlated equilibrium in this game? Consider, for example the signal given to both players not to play ...
Пафну́тий's user avatar
3 votes
2 answers
770 views

Pareto optimality and Externalities

Let's consider 5 farmers, each of them has 2 cows to put into the field. So every farmers can put 0,1 or 2 cows. I denote the three stategies by $q_i$, i=0,1,2. Now, the payoffs ( i.e. the amout of ...
CrishaD's user avatar
  • 31
3 votes
1 answer
70 views

Example of information structure in a one-player Bayes Correlated Equilibrium

Model Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world. The state of the world has support $\mathcal{...
Star's user avatar
  • 446
3 votes
0 answers
49 views

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 ...
Walrasian Auctioneer's user avatar
2 votes
1 answer
187 views

Understanding the properties of extensive form games

In Heller et al, they use the Osborne and Rubinstein formal definition for the extensive form games with public information. To some point they refer to the following two properties $P$ is a mapping ...
Hunger Learn's user avatar
2 votes
0 answers
1k views

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’...
Slim Shady's user avatar
2 votes
1 answer
316 views

Stackelberg setup

I am completely confused because I cannot find the leader's best response. I do not know if it is exactly the same as it was a Cournot game. What I did is: Any help will be appreciated a lot. Thank ...
Stefanos Makridis's user avatar