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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Nash Equilibrium with three players how to solve [closed]

I h Apart from pure strategy nash equilibrium, are there any mixed strategies? If so what are they? why are the no more equilibrium beyond what is found?
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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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Take it or Leave it Offer [closed]

[![I am having a bad time solving second price auctions and lotteries with resale with credit constrains. Does someone know how to answer these?][1]][1] I have to solve some microeconomic bonus ...
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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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asymmetric bid distribution for first price auction with same bid value [closed]

Consider a first price auction with two bidders, bidder 1 and 2. Bidder i’s values are drawn uniformly from [0, i]. Show that if both bidders values are 1, then bidder 1 wins the auction. You can ...
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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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+100

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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Bargaining game of two robbers [closed]

I could not solve the following question. I don't know how to incorporate expectation in expected utility calculations. I would be very happy if you could help me. Consider the following bargaining ...
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2answers
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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
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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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1answer
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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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1answer
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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

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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1answer
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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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1answer
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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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Constructing a game of coordination failure

I was reading the following paper: https://www.econ.nyu.edu/user/debraj/Papers/AdseraRay.pdf It is a short piece and the intuition sounds very clear to me. But my mathematical incompetence is ...
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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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1answer
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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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1answer
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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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1answer
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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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1answer
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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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1answer
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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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Does Nash Equilibrium predict the existence of vaccine reluctance?

I was listening to a lecture on Nash Equilibrium, which stated that a Nash Equilibrium by definition occurs at a point that no players in the game have an incentive to change their strategy - everyone ...
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1answer
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Shapley Value - Any Real World Applications?

The Shapley Value has been around for seven decades now. It is intuitive, tractable, and has many desirable properties. To my surprise, however, its actual applications in the real world are not ...
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Payoffs in games with imperfect information can be different?

I know that a game has imperfect information if there is an nonsingleton information set, and that defines a situation on which a player can't distinguish between the nodes in the information set. ...
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Will the outcome of a game always be a Nash Equilibrium?

Consider this game between two players. This game has two Nash Equilibria: (U, C) and (D, R). Suppose we ask the players to play this game once. What should our prediction of the game's result be? If ...
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Should a sub-game perfect Nash Equilibrium always be a part of the Nash Equilibrium of a game?

I'm solving a 3 person game and the Subgame Perfect Nash Equilibrium I get is not a part of the Nash Equilibrium. Isn't a SPNE supposed to be a refinement over the Nash? I've seen some Nash Equilibria ...
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The role of reinforcement learning in Economics

While working on different research projects I got fascinated by RL which got applied to many fields that are focused on agent based modeling. Though it is a field in Machine Learning what interests ...
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Economics behind reverse auctions with occasional non-profiting suppliers

I was curious about the theory behind a reverse auction system where some suppliers act in a non-profit manner, namely, that their consideration of extra-auctions benefits of providing their service ...
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Von Neumann–Morgenstern implications for repeated strategic games

I am currently studying game theory and have just begun looking at repeated strategic games. In my lecture notes, it states that "preferences are unique up to an affine transformation", ...
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Rationalizable strategies and Weak Dominance

Can I find the rationalizable strategies for a game where none of the players has strict dominance but only weak dominance?
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What is the significance of the findings in Nagel's 1995 paper on Learning Theory?

This post concerns the findings in Nagel (1995). It is a bit outdated but nevertheless still relevant. She examines the Guessing Game, and how individual study-subjects behave in repeated games. In ...
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1answer
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symmetry of equilibria with heterogeneous players

I have a question about game theory terminology. I am working on a model in which players are heterogeneous in two dimensions, and there are four types of players. For example one type of players ...
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Why is this a zero sum game?

The game is described as follows : In a simplified version of the game Morra each of the players shows one finger or two fingers, and simultaneously guesses how many fingerss the other player will ...
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1answer
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Sustainability of Collusion in a finite Bertrand competition with N > 2 firms

In a infinitely repeated Bertrand competition, collusion is sustainable if, and only, if, the following inequality is satisfied, $\frac{\pi}{N(1-\delta)}\geq\pi$ Where $\pi$ is equilibrium profits, ...
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1answer
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Payoff from an option contract

In period 1 the consumer of type $\theta$ selects an option contract consisting of an up-front fee, $B>0$, and exercise price, $\bar{R}$. The consumer pays $B$ at the end of the first period. In ...
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1answer
109 views

Finitely repeated Prisoner’s Dilemma with switching cost

I'm doing this finitely repeated Prisoner's dilemma with switching costs but I have trouble showing the fact that $\varepsilon$ had to be $1 < \varepsilon < 2$. I do see why and that it is a ...

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