New answers tagged game-theory
3
Ariel Rubinstein has a fabulous paper in which he illustrates that Common Knowledge and Almost Common Knowledge are very different!
http://www.cs.cornell.edu/courses/cs6764/2018fa/The_Electronic_Mail_Game.pdf
2
I'd like to understand how this infinite recursion (for lack of a better term...) of knowledge figures mathematically into say, equilibrium concepts.
It figures mathematically, for example, in the simplification of strategy sets through elimination of strictly-dominated alternatives. Others can correct me, but the point isn't to write down a mathematical ...
0
After a while, I have not found conditions or proof the function is quasi-concave at $\alpha \in [0,1]$.
However, the ultimate goal was to show that there is an intermediate solution to the equation. It was indeed possible to condition on the second derivatives w.r.t. to $\alpha$ and $h$ under which:
- the function equals to zero and increases at $0$
- ...
2
First, a caveat: I'm on the job market this year in the midst of the couple weeks when calls are rolling in. Hence, this seemed like a nice way to kill some time (semi-)productively. This is also a disclaimer in case I've made an error :)
Now, let's look at the one you're suggested to try for, where player $1$ chooses $0$ with $p$ and $1$ with $1-p$. Again ...
1
The article Quality of Information and Oligopolistic Price
Discrimination by Liu and Serfes covers this topic in great detail. It also has a rather nice literature review.
1
Captive insurance is an insurance for purpose of insuring the owners of the said insurance. It’s a kind of self-insurance where multiple agents pool their capital together to insure themselves. So the term in that sentence refers to the pool of resources for insurance.
It’s called captive because the modern concept of this kind of insurance was first ...
0
"Steep incentives schemes" are synonymous with "high-powered incentives". A steep incentive scheme is thus one in which there is a large or high-powered performance incentive. This can take either the form of a small fixed payment and a (potentially) large bonus, or it can be a large fixed payment and a (potentially) large penalty for deviation.
Normally we ...
3
It is true that when both principal and agent are risk neutral, the first best can be obtained despite asymmetric information. You should refer to a textbook, such as MWG (ch.14), for the technical details of such models. I'll give an intuitive explanation here. The intuition of the result lies in optimal risk sharing between the principal and the agent.
...
1
From Bolton and Dewatripont Contract Theory (2005, p.135):
"In the absence of risk aversion on the part of the agent and no wealth constraints, the first best can be achieved by letting the agent "buy" the output from the principal."
This quote is in the context of a simple two outcome model.
4
The Key to BNE is that players that know something (about the state of the world or their type) can condition their strategies with their information. That is, for example, in question 3, type A could choose strategy U, while type B could choose strategy D. Therefore from the second player's perspective, there are four possible pure strategies of his ...
2
This thread has some game trees. In case you want put them on your documents, you can do like this (using LaTeX with istgame package):
\documentclass{standalone}
\usepackage{istgame}
\begin{document}
\begin{istgame}[font=\scriptsize]
\setistgrowdirection{east}
\cntmdistance{20mm}{20mm}
\cntmAistb{q_1=0}[at end,below]{q_1=1,000}[at end,above]
\...
1
One way to represent the game tree (assuming that the congressman observes the expert's choice):
The game tree is drawn using LaTeX with istgame package.
\documentclass{standalone}
\usepackage{amsmath}
\usepackage{istgame}
\begin{document}
\NewDocumentCommand\vpay{m}
{ \begin{matrix} #1 \end{matrix} }
\begin{istgame}[scale=2,font=\scriptsize]
\...
1
Just for your convenience
If you are interested in the istgame package, you can do like this (to draw Amit's examples):
For the centipede game:
\documentclass{standalone}
\usepackage{istgame}
\begin{document}
\begin{istgame}
%% for arrows (optional)
\xtShowArrows
\xtShowEndPoints[ellipse node]
\xtHideTerminalNodes
%% some more optional settings
\...
1
I have used LaTeX with tikz package. The following code is used to generate this Centepede Game :
\documentclass{article}
\usepackage{tikz}
\usepackage{bodegraph}
\usepackage[printwatermark]{xwatermark}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=1.3cm,
thick,main node/.style={circle,fill=blue!20,draw,...
2
In direct mechanism agents directly report their preferences (preferences are observable).
In indirect mechanism agents don’t report their preferences directly. Preferences can be observed only indirectly through signals or behavior.
By Revelation Principle if some outcomes can be implemented in indirect mechanism they must be also implementable in the ...
3
If you use LaTeX, you can also draw game trees with the istgame package, which is based on TikZ.
The manual contains lots of examples with full codes including:
game trees in any direction: downwards, upwards, eastwards, -45 degree, etc.
labelling players, action labels, and payoffs
decision nodes, chance nodes, terminal nodes
various information sets
...
2
The dimension of the normal form game derived from an extensive form is given by the number of pure strategies each player has.
Generally speaking, the number of pure strategies a player has in an extensive form game equals the product of the number of actions at each information set where she moves. Suppose a player moves at $N$ information sets on a game ...
3
The center allocation $z_{i}:=(v(N)/|N|)$ for all $i \in N$ is in the core of the symmetric game $v$, whenever $z(S) = \sum_{i \in S} z_{i} \ge v(S) $ holds for all $S \subseteq N$. Now, if $v(N)/|N| \ge v(S)/|S|$ for all $S \subseteq N$, then it holds $z(S) = \sum_{i \in S} z_{i} = |S|\cdot v(N)/|N| \ge v(S)$. Thus, $\mathbf{z} \in C(v)$.
We observe that ...
1
Step 1.
Determine strategies.
Step 2.
Calculate payoffs for strategy profiles.
Step 3.
Write normal form.
2
It depends on what you assume the firms know about each other. Under full information / rationality assumptions, with identical firms, second-mover advantage disappears because the first-mover will recognize the credible threat of undercutting, and set P = MC and that will be that.
If the firms are not identical (e.g., different marginal costs) then turn ...
2
The current mainstream theory of value is the subjective theory of value: goods or services have value that people subjectively believe that they have. Rembrandt paintings cost millions because someone subjectively thinks they are worth that much.
If there are no market failures the market price captures the subjective value through supply demand ...
3
Your conjecture seems to be contradicted, at least for small values of $\sigma$.
You can draw the function with the following R-code:
qq_f = function(x,k,h,sig){
-pnorm(-k, sd=sig)*( (dnorm(h*(1-x), sd=sig))^2 ) - 0.5*dnorm(-k^2, sd=sig)*( 2*pnorm(h*(1-x), sd=sig) -1 )^2
}
curve(qq_f(x,k=0,h=1,sig=0.5),col='blue',xlim=c(-1,3),type='l',main="A ...
2
\begin{array}{|c|c|c|}
\hline
&L&R\\\hline
T&1,1&0,0\\\hline
B&0,0&0,0\\\hline
\end{array}
In the game above, there are two pure strategy Nash equilibria:
$(T,L)$ is an equilibrium in weakly dominant strategies;
$(B,R)$ is an equilibrium in weakly dominated strategies.
Noting that "dominant" and "dominated" are two different words,...
1
You have specialized the definition of BCE in two dimensions: there is only one player, and the player has no private information. If you want to allow for private information you can let the player have some signal $\pi:\mathcal{V}\rightarrow\Delta(T_i)$
And let the decision rule $P_{\mathcal{Y},\mathcal{T},\mathcal{V}}\in\Delta(\mathcal{Y}\times \mathcal{...
2
The concept of the BCE from their 2016 paper is similar to what you have. I think Bergemann and Morris' intuitive explanation is valuable so I'll paraphrase it here.
Each player in the game has a decision rule that chooses an action, $y$, dependent on the state of the world $V$, and the player's information set, which we'll call $S$. This information set ...
1
What is meant by fixed point reasoning here?
Specifically, Nash equilibria. One way to define a Nash equilibrium in words is "a strategy profile from which no player can be made better-off by unilaterally deviating to a different action". In other words, a Nash equilibrium is a "fixed point" because if the game ends up there, play stops because there are ...
0
I'm not an expert in epistemic game theory but let me see if I can help with an example.
Suppose the state space is $\Omega = \{1,2,3,4,5\}$, and there are two players with information partitions
$$
\mathcal{P}_1 = \left\{\{1,2,3\},\{4,5\} \right\} \\
\mathcal{P}_2 = \left\{\{1,2\},\{3,4\},\{5\}\right\}
$$
Suppose the true state is $\omega = 5$.
Let us ...
2
In more detail, payoffs in the table: the first number is associated with the payoff for the first player, the second number on contrary - with the second player's payoff.
Assume the second player plays (K,K), then which one you are going to play? L or R? Of course - L (as $3>2$). Then assume the second player plays (K,U), what is the first player's ...
0
...I'm confused if we can count the root of the contract curve (point M) as one of the efficient points since it's part of the contract curve?
The contract curve is, by definition, the set of all Pareto efficient allocations. Therefore, any point that you choose on this curve--even the end points--is also Pareto effecient.
In this case the indifference ...
Top 50 recent answers are included
