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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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Finding Nash equilibrium [on hold]

$n\geq 2$ individuals have to decide how much capital($y$) to put into their firm, they use the following method. Simultaneously each partner $i$ submits a real number $s_i \geq 0$, the amount of ...
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Maximin from expected utility maximization and common knowledge?

My conjecture is that if 2 agents are in a zero sum game, and they have both agents are Bayesian rational expected utility maximizers. common knowledge of Bayesian rationality and of the structure ...
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1answer
46 views

Cournot duopoly with differing costs

There are two firms in a Cournot duopoly that face inverse demand $P = \alpha - Q$, but one firm has total costs $c_1*q_1$ and the other has total costs $c_2*q_2$ with $c_1 < c_2$. I want to show ...
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26 views

Sender-Receiver games vs Signalling games

Is there actually any difference between Sender-Receiver games and Signaling games? Or these are two different names for exactly the same class of games?
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1answer
121 views

All-Pay Auction Mixed Strategy Equilibrium

I am currently struggling with this exercise. Professor Nash announces that he will auction off a 20 dollars bill in a competition between two students chosen at random. Each student is to privately ...
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1answer
45 views

Proving the existence of Nash Equilibrium using alternate approaches

Most of the standard books/papers/reading materials prove/state the existence of a Nash Equilibrium by appealing to Sperner's Lemma, or to Brouwer's/Kakutani's FPT. However, I've recently come to know ...
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22 views

Prisoners dilemma with N people

I have a prisoners dilemma for N people with such condition. 1) If at least one of the prisoners confesses, then every one of those who confessed will spend in prison one year (gain = V ∈ (0,1)). ...
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2answers
62 views

Is there a game that cannot be represented by a game tree?

Is there a finite game that cannot be represented by an extensive form or a game tree? I know that many games are too long and complex to be represented by a tree of a reasonable size, but that's not ...
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31 views

Mean Field/Differential Game and Measurability

Consider the following scenario. There is a continuum of players in a population, with population measure normalized to $1$. Each player has a type $\theta \in [0,1]$ and we suppose that $\theta$ is ...
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1answer
72 views

Help needed to understand proof in Myerson and Satterthwaite (1983)

The following image is an excerpt taken from Myerson and Satterthwaite's 1983 paper Efficient Mechanisms for Bilateral Trading: I know what the theorem is all about, all I need is some help with the ...
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1answer
54 views

Game Theory; Finding the Nash Equilibria

How to proceed with such problems where there is no pure Nash Equilibrium? Even if we attempt to eliminate strictly dominated strategies, we find none.
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3answers
164 views

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 ...
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Are there any experiments about financial games with just one player?

I was wondering if there are any experiments of financial games (laboratory games under controlled circumstances like Plott and Sunder's Rational Expectations and the Aggregation of Diverse ...
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1answer
29 views

General Results on First or Second Mover Advantage?

I am just wondering whether the following question has already been answered in game theory: Fix an arbitrary (say, finite) two-player strategic form game. Under what condition, does one player (say, ...
2
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1answer
34 views

Is it possible to have transferable utility in non-cooperative games?

Transferable utility is a concept that seems to be associated with cooperative game theory and coalitions. I would like to know if there are any examples of transferable utility in non-cooperative ...
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0answers
27 views

Query regarding best response curves

Hal Varian intermediate microeconomics ch-29(game application), page-546 to 550, subheading-games of competition. 1) in page 548, to quote the author "what about column? We can perform a similar ...
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2answers
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Straffin, P. D. (1993): Game Theory and Strategy. How is the security level on p. 103 calculated?

Could somebody explain how Straffin calculated the security levels for Rose and Colin on p. 103? As far as I understood, Colin's security level is 6 because it is the minimum of the strategy Colin A ...
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0answers
64 views

Insurance question: need a brief explanation

Two risk averse people are identical in every way (including wealth, W , amount of loss, L, and utility function, U(W)) except they have different probabilities of loss. Suppose they want to buy ...
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1answer
48 views

First Price Auction with Reserve Price

I'm trying to solve the following question: "The seller wants to auction off a single item to two bidders, the valuation of each bidder is an iid draw from a uniform distribution on $[0,1]$ where ...
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0answers
59 views

Signaling questions (separating equilibrium)

Consider two firms Inverse functions: $p(q)=max\{a-q,0\} $ $q$ is total production and a is positive constant. This value of a takes two values ah=2 (high demand) and aL=1 (low demand). Their ...
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1answer
32 views

Why is every action considered to be in the support while calculating mixed strategy equilibrium?

While evaluating the mixed strategy equilibrium, in most of the cases, we consider that all actions of a player are in the support of the equilibrium.Is it always so? I was going through a problem (...
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1answer
60 views

Market Power in microeconomic theory

What does the term Market Power mean in microeconomic theory
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1answer
86 views

Discount function

Company A needs to provide service $p$ to company B. However if the company B will reserve the $(1-\alpha)$ fraction of resource for the serving customers of company A, company A will provide a ...
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3answers
56 views

Is choosing an investment by a bank only due to its regulatory capital charge a form of moral hazard?

The main shortcoming of the first Basel Accord (Basel I) was that its capital requirements did not reflect the actual risk of the bank assets. One way this nonsense influenced the asset choice of ...
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0answers
41 views

Perfect Bayesian vs sequential equilibrium

when do we use the concept of the Sequential Equilibrium and when do we use the concept of perfect Bayesian Equilibrium to solve a problem? (for example when we have a game tree like the one in the ...
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0answers
36 views

Two-sided market and bargaining game

I am solving a bargaining problem in which I have two players $player_1 $ and $ player_2 $. Both of them have a service (represented as $ z_1 ,z_2 $) that they can provide . Moreover they will ...
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1answer
139 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 ...
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1answer
187 views

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 ...
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1answer
102 views

Subgame perfect equilibrium and expected profit

I am so confused because I cannot set up the monopolist's profit maximization problem.What I did is the following one: Any help will be appreciated. Thank you.
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0answers
185 views

How can I determine if a token economic is viable?

Given a system where you incentivize people to do actions in a system, we might have good and bad actors. I would like to know if there is a software or framework where I could put the different <...
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1answer
32 views

Location game between 3 firms

I could solve Question 25 (simultaneous location game between 2 firms), but I'm confused between options b) and d) for Question 26 (sequential game involving a third firm). I have attached both ...
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1answer
195 views

Finding the optimal tax

I have a problem regarding the last two questions of this exercises because I can not understand how to set up my model in order to find the optimal tax the optimal quantity to be as there was not a ...
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0answers
42 views

How to find sequential equilibria and weak perfect bayesian equilibria quickly?

I have read several texts on the nature of sequential equilibria and weak perfect bayesian equilibria (called such by Mas-Colell, also called weak sequential equilibria). I am not looking for ...
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1answer
159 views

How are ties broken in a second price sealed bid auction?

Say there are two people who evaluate an object at 5 dollars and a third who evaluates it at 4 dollars playing a second price sealed bid auction. The first two bid 5 dollars and the third bids 4 ...
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2answers
229 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 ...
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1answer
436 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) $\le 0$ ...
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24 views

Equivalent Texts to Tirole's Game Theory

What are some books that are on par with Tirole and Fudenberg's Game Theory, excluding Myerson, Camerer, and Sinervo & Friedman? Obviously, all these books take a different perspective on game ...
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1answer
36 views

Repeated game with stage game has more than 1 NE

Given the game like Prisoner's dilemma (infinitely undiscounted) and each person has 3 actions in every period: confess defect and kill, and the payoff matrix have 2 NE as (D,D),(K,K). Can I still ...
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1answer
261 views

3 Firm Stackelberg's Oligopoly Game

Consider a market in which there are three firms, all producing the same good. Firm i's cost of producing qi units of the good is Ci(qi)=0 for qi≥0 for each i∈{1,2,3}; the price at which output is ...
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2answers
192 views

Finding subgame perfect equilibrium

The main part of the question is as follows (if you cannot read this, I can immediately write it) My question is how to find the subgame perfect Nash equilibrium for the both cases $\bar{g_2}\ge \...
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0answers
30 views

Game of Price Gouging (1st Degree PD)

I am currently modeling a game that shows price gouging is socially beneficial under the right conditions. The question is, I am only evaluating one good and not the classic two good case, so should ...
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1answer
132 views

Game theory - Write a maximization problem (with restriction)

I have a problem with finding a way how to solve this example: We have the company, which has two types of customers indexed as $H$ and $L$. We assume: $θ_H > θ_L$. Quantity$(Q)$ of $H$ indexed ...
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0answers
27 views

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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1answer
122 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 ...
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1answer
100 views

Cournot equilibrium question

There are two firs in the market. They produce perfect substitutes at cost $c(y_i)=y_i/3$ for i=1,2. The demand function is $p=1-(y_1+y_2)$ Consider the Cournot competition where firms ...
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1answer
65 views

Auction question

I’m studying on auction. But I couldn’t understand some questions about this topic. And I cannot solve such type questions. For example, I know that a set of symmetric and risk neutral bidders ...
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1answer
69 views

Finding Bertrand equilibrium with no demand function explicitly given

Two cell phone companies A and V are located at the extremes of a line of length one and transportation cost t = 4. Consider an initial situation where both firms offer a generic phone that consumers ...
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1answer
131 views

Mixed Nash equilibrium

I have game table posted below: $$\begin{matrix} &\#2 \\ \#1 & \begin{array}{c|c|c|c} &D &E &F \\ \hline A &4,4 &6,6 &2,6 \\ \hline B &6,4 &2,2 &0,4 \\ \...
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1answer
185 views

Question on subgame perfect equilibrium

Consider a world of complete information with two agents X and Y and two time periods 1 and 2. Person X only lives in second period. Person Y lives in 1st and 2nd periods both. X and Y are each ...
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2answers
64 views

Proper definition of extensive form game

Consider the following game: Let $N := \{1,2,3,4\}$ denote a set of agents. Going from 1 to 4 each agent can decide how many of the remaining agents he wants to integrate into a coalition. The ...