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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What theory fits?

IO & game theory friends, I am thinking about a setup where there is many buyers and a decent number of sellers (they have pricing power). Goods and buyers' preferences are homogeneous and known. ...
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Alternative way to calculate the symmetric BNE of the game

My problem. Consider the following auction for a single object. There are $n \geq 2$ bidders. They submit their bids simultaneously. The object is allocated to the player who submits the largest bid. ...
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Job Market Signaling

My Solution is this Separating equilibrium High type worker chooses $e_H = e^* >0$ Low type worker chooses $e_L =0$ Firms believes that if education is $e^* >0$ then the worker is high type and ...
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Where can I learn random matching models?

The title says all. I need papers or textbooks that explain in detail (step by step, maybe showing some canonical results) how I can model random matching games. Does anyone have a reference? Thank ...
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Nash bargaining solution textbook treatment

I'm looking for some reference that treats the solution that Nash gave to the bargaining problem in which two parties must share the surplus derived from engaging in a cooperative relationship. ...
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Effect of bounding action space on the set of equilibria

Suppose $N$ players play a game, where each player's action space is $[0,1]$. Each player has an identical continuous utility function $u:[0,1]\times [0,1]^{N-1}\rightarrow\mathbb{R}$, where the first ...
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The intuitive criterion

I have asked a similiar question before, but I would very much appreciate if someone would say if my reasoning in this particular case is correct. Consider the down below: For part a) I have found ...
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What's the difference between Ex-post Incentive Compatibility and Dominant-Strategy Incentive Compatibility

According to the Wikipedia definition of Dominant-Strategy Incentive Compatibility (DSIC): DSIC means truth-telling is a weakly-dominant strategy, i.e. you fare best or at least not worse by being ...
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How to find pure strategy NE if you have a n X n matrix (n players) [closed]

Consider the down below which I have trouble with solving. I am not used to find NE for n players, but rather for a simple $2 x 2$ matrix or $3 x 3$, but how does one find NE when you have N players? ...
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How to show that a strategy is a SPNE in repeated games

Consider the down below which I have trouble with solving. For part 1) I have said that a possible outcome path is to play $(D,D)$ in the first round and for all rounds following until $i \leq 298$. ...
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How to understand the intuitive criterion

I am studying for my exam in MicroEconomics 2 which involves game theory and I have trouble with understanding the intuitive criterion and how to use it. Consider the down below signalling game. ...
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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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Find SPNE for the extensive game with imperfect information

Find SPNE? My suggestion is $\{(AW,L,Y), (BU, L,Y), (BD,R,Y)\}$ How to find : firstly, I consider the first subgame where P3 and P1 play. And I choose (W,Z) Secondly, I consider the second subgame ...
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BNE: Incomplete Information Cournot

Consider two risk-neutral firms that compete in quantities (Cournot). The aggregate inverse demand is given by $P(Q) = 3-Q$. Each firm can only observe its own cost. Find a symmetric BNE. The constant ...
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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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Rule for Number of Strategies in Bayesian Games

Is there a general rule for finding the number of strategies (denote as $S$) for each player in a Bayesian game? I think it's related to the number of types (denote as $T$) and the number of actions (...
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On the (rather strange) notion of strategies in repeated games

As undergraduates often note, the definition of a strategy appears to be rather strange in the context of repeated games. To illustrate, consider a very simple game in which one player needs to make a ...
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Cournot nash equilibrium

The market demand for a good is described by the inverse demand function $P(Q) = 120 - Q $ where $Q$ is total quantity demanded and $P(Q)$ the market price. Two firms $i =1,2$ have identical cost ...
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Betting on the sum of scores

Here is a game I like to play: Every player gets a random number independently drawn from a fixed distribution. To fix ideas, suppose everyone draws a number from $\{2, ..., 10\}$ where all numbers ...
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A question related to purification theorem

I am stuck at some point in part b, I would be very happy if you could help. My calculations are below the question. a) P1 plays N with probability p. P2 plays N with probability q. Mixed Nash: $((\...
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Pure Nash equilibrium in bidding game?

According to the answer key for a problem set, there is no pure strategy Nash equilibrium in the following problem. Yet I can't see why not. Could it be an error in the answer key? Here's the problem: ...
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Perfect information game

Assume that there are two parents A and B who are tempted to pick up their children late. We denote the set of parents $N = {A, B}$. Each parent $i \in N$ chooses from the action set $A^i = {E, L}$ ...
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Showing existence of a Nash equilibrium in pure strategy

Consider a game with $N$ players, each indexed by $i=1,...,N$. Every player $i$ has to choose a $J\times 1$ vector of actions $a_i\equiv (a_{i,1},...,a_{i,J})$ where each $a_{i,j}$ can be zero or one. ...
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Bertrand game with delivery risk and side payments

Consider three agents $A_i$, who engage in a Bertrand game. All agents have perfect knowledge on all parameters and the distribution $F()$. $A_1$ moves first and selects price $0\leq p_1\in \mathbb{R}...
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Two Sellers, One Buyer Auction

Consider the following game. There are two sellers, each of whom can produce one unit of an indivisible good. The cost of producing the unit for seller i is $c_i$ . There is a single buyer who wishes ...
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Auctions and finding nash equilibrium of a dynamic game

Suppose we have a sequential version of an Auction game: • Player 1 places a bid. • Player 2 observes player 1’s bid, then places a bid. • The player with the highest bid wins the item at auction. • ...
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Revelation principle when the type space is infinite [closed]

Consider a mechanism design problem in which the agents have type spaces that are uncountably infinite. I have a couple of questions which are numbered throughout this post. The revelation principle ...
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1answer
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Characterising a set of outcomes containing the collection of pure strategy Nash equilibria

Consider a game with $N$ players, each indexed by $i=1,...,N$. Every player $i$ has to choose a $J\times 1$ vector of actions $a_i\equiv (a_{i,1},...,a_{i,J})$ where each $a_{i,j}$ can be zero or one. ...
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1answer
48 views

Form of security with a potentially infinite amount of equity for a continous payout for game?

I'm trying to create a game that's a bit like monopoly. The objective of the game is to earn money by investing money. The game has a limited amount of players and an increasing amount of money each ...
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Nash equilibrium with three players

Consider the game below played by three players. Player 1 chooses one of the rows (T vs B). Player 2 chooses one of the columns (L vs R). Player 3 chooses one of the three tables (A vs B vs C). Each ...
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Bayesian Nash Equilibrium in a Duopoly Cournot Competition

I am having a hard time to solve a Bayesian Nash equilibrium game in a duopoly cournot competition setting. So, I have two firms with given production quantities, let's say $q_1$ and $q_2$ (i.e., not ...
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Effect of exogenous parameter on three player SPNE profits

Consider three agents $A_i$. $A_1$ moves first and selects $0\leq q_1\in \mathbb{R}$. $A_2$ moves second and selects $0\leq q_2\in \mathbb{R}$. $A_3$ moves third and selects $0\leq p_1\in \mathbb{R}$ ...
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Game Theory: Continuity in equilibrium profits?

Consider 2 agents $A_i$. $A1$ moves before agent $A2$. Each of their utility functions is continuous in each agents' decision $0<s_i\in \mathbb{R}$ and a parameter $x$. Additionally, each agent's ...
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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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Multi dimensional Auction in economics

I am following this paper . They have different suppliers and one buyer and They are using auction to select best suppliers Suppliers will submit. suppliers offer a multidimensional bidding on quality ...
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Find a separating perfect Bayesian equilibrium

Exercise Question 2, Chapter 28, Strategy: An Introduction to Game Theory 3rd Edition by Joel Watson In part (a) of the question, we have to check if any separating perfect Bayesian equilibrium ...
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Strong sequential equilibria and the existence of others

I am working on the following game and I have to find all strong sequential equilibria here. I determined that here any belief derived from a fully mixed strategy gives a distribution (1/2, 1/2) over ...
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Simultaneous vs Sequential Games [closed]

Is there a way to characterize the distinction between simultaneous vs sequential games? I'm trying to describe a situation where players can only take actions without knowledge of other players' ...
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If a best-response dynamic converges, does it converge to a Nash equilibrium?

Consider a game with a finite number of players and finite action space. Suppose we consider a sequential iterative game-playing process in which, in each period, players myopically select actions ...
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Find the set of Pareto efficient payoffs in game theory [closed]

Here I want to find Pareto efficient payoff set. The answer is (C,β), (B, β), (C, δ) But I don’t understand why? Please explain clearly this answer. Thanks a lot
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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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Relaxing the notion of Nash Equilibrium

Consider a game with $N$ players, each indexed by $i=1,...,N$. Every player $i$ has to choose a $J\times 1$ vector of actions $a_i\equiv (a_{i,1},...,a_{i,J})$ where each $a_{i,j}$ can be zero or one. ...
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Topology on the space of measurable functions

The context is as follows: Suppose we have a 2 period sequential game, with player $i$ in stage $i$, with action set $A_i$. Give $A_i$ all the nice properties, as compact, separable metric spaces (I'd ...
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Differences between best response, dominant strategy and Nash equilibrium

I can't seem to get the differences of these terms. I watched this video that has the differences of best response and Nash equilibrium: But then I heard about dominant strategies from another video ...
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Can't find the SPNE

For a homework assignment, I need to find the subgame perfect equilibrium. The assignment asserts that there is only one subgame perfect equilibrium in this problem, but I am stuck between two ...
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Can vaccine distribution and appointment setting up be considered game theory?

New to game theory and I started thinking about the difficulty of setting up an appointment for the covid vaccine. Could this be something to study in game theory? Would we need to figure out the Nash ...
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Is there really a Nash equilibrium in this example?

I was watching this video on Coursera and worked out the example before the solution was presented. The example begins at 4:20 The presenter says that the Nash ...
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How to Represent as a Payoff Matrix

I'm trying to represent the following as a pay-off matrix. I have 100 dollars to invest in one agricultural stocks with a choice of apples, pears or grapes. Return on investment relies on whether ...
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Comparing & contrasting decision problems and normal games

I am trying to compare and contrast between decision problems and normal games. Are there any key concepts I should know? Any help would be greatly appreciated.
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How to set up the payoffs properly for a division of labor game

I'm admittedly a novice when it comes to game theory (currently a few lectures into Yale's intro course lectures), so hopefully people will indulge me what may be a dumb question. I was trying to ...

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