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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Two case studies of companies accused for refusing to pay money

Case study 1: A is a television manufacturer company. B is a company which manufactures capacitors. A sent a contract to B for producing capacitors for A's televisions and in return A will pay for it....
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25 views

Two Players Different Strategies in infinitely repeated game

I am vexed by a Game Theory question regarding infinitely repeated games. Usually, strategies such as Grim Trigger or Tit-for-Tat are discussed in a context where both players have the same strategy. ...
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Illustrating difficulty to find dominant strategies: series of simple one-shot two-players games

For a game theory class I am prepping, I am looking for simple mathematical puzzles that can easily be presented as one-shot 2-players simultaneous games in which one of the players has a dominant ...
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1answer
40 views

Value Function For Durable-Good Monopolist with General Distribution

It is known that with a unit mass of consumers, each of whom has a value distributed between 0 and 1, one can think of the monopolist solving \begin{equation} \max_{p} \ p[1-F(p)] \end{equation} when ...
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Maximum-support Nash equilibria in zero-sum games

Context: I would like to know how likely a player is to pick a specific action, provided that he plays optimally and the action is optimal. Phrased like this, the question is ill-defined. But is there ...
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61 views

Airport problem

Assume that there are $m$ different types of aircrafts. For each type $l$, we know the number of movements, $n_{l}$, and the overall runway costs, $c_{l}$, associated with type $l$ aircrafts. Since we ...
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25 views

Is a combination of Political economics and Game theory possible and beneficial?

By Political economics I do not mean the "economical" advice given by some people(see the Wealth of Nations by Adam Smith) but rather the heavily mathematized subfield of Economics studying and trying ...
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1answer
23 views

How to solve for the potential of a cournot duopoly problem?

So i have this question And i have no clue on how to get to verifying that that function on the answer sheet is a potential Cournot game. I started answering the question like this, but then i got ...
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1answer
27 views

Robust predictions in single-agent decision problem with uncertainty

I would like your help to better understand the possibility of using the notion of Bayes Correlated Equilibrium (BCE) in a single-agent decision problem with uncertainty to make predictions on optimal ...
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1answer
56 views

Confusion about multiple information Sets

I'm confronted with the following situation: First of all nature decides which of two games is played. Then each of two players make a simultaneous move, but only player I knows which game is played....
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56 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 $N$-...
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1answer
45 views

Monotonicity of second price auctions with bidder-specific reserve prices

I am having difficulty understanding the problem below: Given CDFs $F_1, ..., F_n$, prove that the allocation rule of a second-price auction with bidder-specific reserve prices is monotone. The item ...
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1answer
27 views

I cannot find for this Simple shared effort level game

Each player can contribute to the project with non-negative effort. Player 1's utility is $u_1=e_1(1+e_2-s\cdot e_1)$ where $s\in [0,1]$. Player 2's utility is $u_2=e_2(1+e_1-e_2)$ For case 1, ...
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1answer
34 views

The difference between a Nash equilibrium and Bayesian Nash equilibrium [closed]

What is the basic difference between Nash equilibrium and Bayesian equilibrium?
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1answer
67 views

What is the most general definition of “the core” in game theory?

I’ve seen definitions of “the core” that rely on some specific assumptions, such as that the game is one of a transfer of resources, or that there is “transferability of utility” (presumably intending ...
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1answer
37 views

Sequential Game is Extensive form game?

Dynamic, Sequential, Stochastic, Extensive form and Evolutionary games. I know what all of them mean very roughly. I want to clarify them. As I understand Extensive form is a description of a ...
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16 views

Subgame perfect Nash equilibrium with incomplete information [duplicate]

Take the following two-stage game with incomplete information and simultaneous actions in each state. (1) In the beginning of stage 1 players 1 and 2 do not observe the value of $\epsilon$ but they ...
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1answer
29 views

Definition of subgame perfect Nash equilibrium

Take a two-stage game with complete information and simultaneous actions in each state: (1) Player 1 and 2 simultaneously choose action $a_1\in A_1$ and $a_2\in A_2$ respectively. (2) Player 1 and ...
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26 views

Fehr & Schmidt, ultimatum game, inequaltiy aversion, perfect subgame Nash equilibrium

I am preparing for an exam. I have found an old exam but I have no solutions for it, so I tried to solve it, but I dont know if I did it correctly and need therefore your help. The problem looks as ...
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1answer
36 views

Convert a sequential move game into a simultaneous move game

A statement from Ponssard and Zamir "Zero-sum sequential games with incomplete information" at the bottom of the first page reads AM's result is for zero-sum two-person games in which the two ...
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1answer
36 views

NASH equilibrium [closed]

How to approach questions like these: In a two player static game with a discrete strategic space that permits each player to chose one of the four possible strategies what is the maximum number of ...
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26 views

Stay or switch game

Consider a game consisting of two players, P1 and P2, played over multiple time steps. Refer to P1 as she and P2 as he. State: Each player can be at one of two locations, A or B. Writing the possible ...
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1answer
44 views

Clarification on the definition of Bayes Correlated Equilibrium

I would like your help to understand the definition of Bayes Correlated Equilibrium (BCE) in an incomplete information game at p.7 of this paper. Let me summarise the definition provided in the paper....
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1answer
69 views

Stackelberg Oligopoly 3 firms [closed]

Imagine that there are 3 firms in a monopolistic market, F1, F2 and F3. Firms 1 and 2 are incumbent firms and act simultaneously whereas Firm 3 observes the actions of both firms before deciding ...
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1answer
20 views

Implications of the concepts of combination/expansion of an information structure

I would like your help to understand the concept of combination/expansion of an information structure in the incomplete information game at p.6-9 this paper. Let me summarise the game as described in ...
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1answer
42 views

Sequential game equilibrium strategy question

The question asks for player B's equilibrium strategy, hence shouldn't player B choose the strategy that gives the highest payoff after player A's move? Why does player B choose 4 over 5 and 6 over 8 ...
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26 views

Optimal pareto in two-person game

For what values $x$, $y$ the profile $(D,L)$ is Pareto optimal? \begin{array}{c|ccc} & L & R \\ \hline U & x,5 & x+2,y \\ D& 1,-1 & x,0 \\ \end{array} Is correct $x<1$ ? ...
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25 views

Condition for a Nash equilibrium

Consider two people have a mutually advantageous relationship. That is, if both dedicate more effort to the relationship both improve. Specifically, each individual chooses a level of effort $x_{i}\...
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1answer
45 views

Construction of a 3x3 simultaneous game

How could I construct a 3x3 simultaneous game with 2 players with no equilibrium in pure strategies but 1 is mixed strategies . I am able to write down one with no pure strategy Nash equilibrium but ...
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32 views

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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1answer
17 views

Rationalizability or Nash equilibrium

In the 'chicken' game, (stop,go) and (go, stop) are the two pure strategy Nash equilibrium profiles. If the game is played once, does it make more sense to use the rationalizability solution concept? ...
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1answer
29 views

Credible Threat in the Perfect Bayesian Equilibrium

Consider a simple game between P1 and P2 shown in Figure 1. We consider a Perfect Bayesian Equilibrium. P1 uses a cutoff strategy based on his $c_1$ that has the Cumulative Distribution Function of $...
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55 views

What is the game theory of retaliatory trade tariffs?

Suppose no tariffs, or negligible tariffs, exist between nations A and B, and suddenly A introduces substantive tariffs on certain products A imports from B. In theory, this could lead to B and A ...
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1answer
40 views

The concept of expansion of an information structure

I would like your help to understand the concept of expansion of an information structure in the incomplete information game at p.6-9 this paper. Let me summarise the game as described in the paper. ...
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2answers
135 views

The concept of information structure in incomplete information games

I would like your help to understand the concept of information structure in the incomplete information game at p.6-7 of this paper. Let me summarise the game as described in the paper. There are $...
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1answer
151 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 \...
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1answer
32 views

mixted strategy that assigns positive weight to a pure startegy that is dominated

This problem is of Fernando Vega Redondo(Economics and the theory of games) Exercise 2.1 Let G be a game in strategic form. Prove that, for every player $i\in N$, every mixted strategy $\sigma_{i}\...
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64 views

Are there strictly dominated strategies?

Two players simultaneously announce a prime number less than 20.Denoting $p_{i}$ the number announced by the player $i$, the payoffs are: -If $p_{1}+p_{2}<14$ each player receives as payment the ...
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1answer
33 views

Obligations of a company

Any company may "feel" obligated towards several parties at once: its shareholders its employees its customers its partner companies (sub-contractors and suppliers) its country and social environment ...
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1answer
24 views

Is anyone familiar with the following basic resource sharing model?

Here is a resource sharing model, I do not remember where I came across it, I am wondering if this is well known in econometrics. Let $T > 0$ be the total quantity of resources. For example, ad ...
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30 views

Interpretation of Solution Concepts

I was wondering whether there is a neat overview over different interpretations of game theoretic solution concepts such as Nash equilibrium, Sequential Equilibrium and the like. Textbooks I found ...
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53 views

Is truth cheap, and falsehood expensive and volatile? [closed]

Question: In a scenario where data is bought and sold in a double-auction market, will the trading price and volatility of a given piece of data become inversely proportional to its accuracy over ...
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42 views

Game Theory: finding nash equilibria of an extensive form game (game tree) [duplicate]

How do you find the pure Nash equilibria from this commitment game? The SPNE is (U, ps) Do you find the NE by finding the best response (BR) of a player to a specific strategy of the other player? ...
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38 views

How to approach such question of two periods and asymmetric information game?

There are two players 1 and 2, playing a two-period public good contribution game. The benefits from the public good per-period to each player is $b_1$ and $b_2$ respectively, which are common ...
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1answer
251 views

Bayesian Nash Equilibria in Battle of Sexes

Consider the static Bayesian game as described above. $\ t_1$ and $\ 𝑡_2$ are the types of the row and column player respectively, which are both uniformly distributed on the interval [0,1]. The ...
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1answer
64 views

Symmetric Cournot equilibrium: suffciency without second order conditon

Let $q_i \in Q = \mathbb R_+$ denote the quantity produced by firm $i \in \{1,2\}$. Further let $\pi_i(q_1,q_2) = (1-q_1-q_2)q_i$ denote the profits of $i$. A Nash equilibrium $(q_1^*,q_2^*) \in Q^2$ ...
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25 views

Is second price auction better than first price sealed bid auction? Why? [duplicate]

As I understand and have read the advantage of the 2nd price auction is that it encourages bidder to bid for 'true value', which I think can also be done with the 1st price sealed bid auction. I might ...
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1answer
48 views

Cournot's game profit maximisation first order condition question

My question is about the last part (I attached the rest for context). I don't understand the final line at all. I thought the first order condition would just be to set the derivative = 0. Very ...
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1answer
139 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 $\epsilon_i$. ...
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1answer
47 views

Spence's Job Market Signaling Game

I have a little doubt in the Job Market Signalling Game. I am referring to A Primer in Game Theory: Gibbons, Chapter 4, Signaling Games The attached paragraph refers to a Separating Equilibrium case ...