Tagged Questions
3
votes
1answer
36 views
Stability under supremum of sets of social choice function with single peaked preferences
Here is a question emerging from reading Moulin, H. (1980). On strategy-proofness and single peakedness. Public Choice, 35(4), 437–455.
The setting is as follows:
A non-empty finite set of ...
0
votes
1answer
31 views
Using limit argument with non-continuous social-choice functions
This question is related to another question of mine Invariance of strategy-proof social choice function when peaks are made close from solution, and it revolves around the use of limit arguments with ...
6
votes
1answer
58 views
Invariance of strategy-proof social choice function when peaks are made close from solution
A question emerging from reading Schummer, J., & Vohra, R. V. (2002). Strategy-proof Location on a Network. Journal of Economic Theory, 104(2), 405–428.
The setting is as follows:
A finite set ...
1
vote
1answer
36 views
Concept of efficiency in auctions
I have some confusions about the concept of "efficiency" in auction theory.
One interpretation is that an auction is efficient if it maximizes the social-welfare. But social-welfare is not well ...
4
votes
2answers
67 views
Does Arrow's Theorem apply when choosing a single best candidate?
According to Wiki, Arrow's Impossibility Theorem proves that we cannot create a social welfare function that obeys unanimity, non-dictatorship, and IIA.
However, in real elections, we want to choose ...
0
votes
1answer
82 views
Find profit maximizing profit and quantity given willingness to supply curves and a merger
This is a homework problem, but I'm at my wit's end. I don't even know where to start on this, but I've tried a number of strategies.
Consider a regional market for wholesale electricity where ...
1
vote
2answers
121 views
Cournot-Nash Equilibrium in Duopoly
This is a homework question, but resources online are exceedingly complicated, so I was hoping there was a fast, efficient way of solving the following question:
There are 2 firms in an industry, ...
4
votes
1answer
81 views
Gibbard–Satterthwaite Theorem versus Arrow Theorem
Arrow Theorem is a very classical result in social choice theory, stating very roughly that any reasonable voting procedure is either dictatorial or subject to tactical voting. More precisely, there ...
1
vote
0answers
42 views
Game theory question- information quality maximisation, opinions of the question
I am developing a game theory question to help in deconstructing situations where information quality is comprimised and requires valuation against a set of criteria. I would be interested to know any ...
2
votes
0answers
80 views
What is the (expected) outcome of this hybrid auction?
A certain hybrid auction can be accurately modelled as follows.
There are $n$ risk-neutral, rational participants $i=1,2,\ldots,n$, and a guy called Zerro: $i=0$.
Each, except Zerro, has a private ...
3
votes
1answer
129 views
Finding mixed Nash equilibria in continuous games
I'm taking my first (graduate-level) game theory class. I understand how to find Nash equilibria in simple games, such as those given in finite tables, and can see (usually) how to find the mixed ...
1
vote
2answers
297 views
Game theory: Nash equilibrium in asymetric payoff matrix
I have a utility function describing the desirability of an outcome state. I weigh the expected utility with the probability of the outcome state occuring. I find the expected utility of an action, a, ...
1
vote
1answer
68 views
Mathematics behind Incentive Design
I was working on an Applied Math project on allocation and I had an interesting idea about extending it to providing incentives to different "players" in the allocation process.
But I am clueless ...
1
vote
1answer
67 views
vickery auction question(second-price auction)
The question is as follow,
Alice and Bob would both like to own the same manuscript. The manuscript is worth 5 million to Alice and worth 3 million to Bob. The present owner of the manuscript ...
0
votes
1answer
79 views
subgame perfect nash equilibrium for war of attrition
the question is as follow:
suppose that two players are playing war of attrition,
that means both of them could choose either to fight or quit, if either one of them quit, the game ends, and if ...
1
vote
2answers
782 views
cournot competition with N-firms
The question is as follow:
Here is how we can think of N-firm Cournot competition. Assume all the firms have the same marginal cost C > 0. Firm 1 chooses Q1, Firm 2 chooses Q2, and so on. The market ...
1
vote
0answers
87 views
Cournot-game problem
I'm so stuck with an exercise about Cournot game and was hoping if someone could help me out here. Would appreciate all the help. This is the exercise:
Consider the market for Blue Turtle (a new ...
2
votes
0answers
66 views
Optimal strategy in a VCG auction with partial collusion?
Suppose you control the bid prices in a multiple-item VCG auction for a partial coalition of bidders. Each bidder is only allowed to win one item out of the set of multiple items, which are all ...
1
vote
1answer
122 views
Question on mixed nash equilibrium!
The question is as follows:
Think of the Golden Ball game. Now player 1 is money-minded and jealous, and player 2 is very good-hearted, so the payoff matrix is follows:
...
2
votes
1answer
117 views
Economics: two rival firms in two countries
I am currently working on a paper in macroeconomics, where I found a result that I cannot manage to understand. Since we don't have a macroeconomic site yet, and this is mostly game theory, I will ...
2
votes
0answers
89 views
proof using (fixed point theorem)
I am seeking to solve for a Nash equilibrium in pure strategies $(d_2,d_2)$ involving two players, $1$ and $2$. Given that $h'(.)$ is s strictly decreasing and continuous function, $\Phi(d_1-d_2)$ ...
0
votes
2answers
400 views
Subgame Perfect Nash Equilibrium
My homework question is summarized below:
There are 7 players (say P1,P2,...,P7) trying to split 100 dollars. The game starts with P1 proposing an allocation of the 100 dollars to each ...
5
votes
0answers
175 views
Olympic Badminton, or How to Design a Tournament
Hearing the recent news about disqualified Badminton players in the ongoing 2012 London Olympics got me wondering about how best to design tournaments to avoid situations where players are ...
0
votes
1answer
213 views
Finding Nash Equilibria with Calculus
The problem is summarized as:
There are two players. Player 1's strategy is h. Player 2's strategy is w. Both of their ...
1
vote
1answer
285 views
Unable to find Nash equilibria in mixed strategies
Here is the strategic form game:
Player 2
Left Middle Right
Top 2,2 0,0 1,3
Player 1 Middle 1,3 3,0 1,0
...
0
votes
0answers
52 views
what exactly does symmetric game and symmetric equilibrium mean?
I am confused about the ideas of a symmetric game and symmetric equilibrium of a game under the following conditions.
1) pure strategy Nash equilibrium
2) Nash bargaining game where players set a ...
1
vote
2answers
173 views
summation notation for general sets
I'm working through an academic game theory paper and stumbled upon this summation notation in a proof and I'm not quite sure what it means:
$$\sum\limits_{j \in M \backslash\ \{i\}}$$
There is a ...
1
vote
1answer
72 views
Nash equilibria of mixed strategies
I am given the following game to find nash equilibria in pure and mixed strategies:
$\begin{pmatrix}& & Litte John &\\ & & c & w \\Big John & c & (5,3) & (4,4) \\ ...
4
votes
2answers
1k views
Cournot Nash Equilibrium Between Two Firms
Suppose we have two firms with specialized, but similar products. Suppose market demand for the two products is:
$$p_1(q_1,q_2)=a-bq_1-dq_2$$
$$p_2(q_1,q_2)=a-bq_2-dq_1$$
where $d \in (-b,b)$. Suppose ...
2
votes
0answers
211 views
Nash equilibrium question
(Hotelling’s voting model) Consider a population of voters uniformly distributed along the ideological spectrum from left (x = 0) to right (x = 1). There are two candidates i = 1,2 for a single
office ...
3
votes
2answers
294 views
Finding best response function with probabilities (BR) given a normal-matrix representation of the game
We are given players 1, 2 and their respective strategies (U, M, D for player 1, L, C, R for player 2) and the corresponding pay-offs through the following table:
$\begin{matrix}
1|2 & L & C ...
5
votes
1answer
221 views
Measure of value of resources in a competitive game
Let we have a competitive survival game in which a player has choice between different resources to earn. The question here is which resource should he prefer to maximize the chance of survival. I ...
