Questions tagged [dynamic-games]
Questions related to the application of game theory to situations in which actions are taken sequentially.
38
questions
1
vote
0answers
39 views
Why Sequenial Equilibrium (SE) imposes no restrictions on the off-equilibrium beliefs in the Spence's model?
I read some lectures on the Spence's model. Some (see e.g. P31 of lecture PPT from MIT game thoery course) mention that SE imposes no restrictions on the off-equilibrium beliefs but without proof. I ...
3
votes
1answer
36 views
Design of efficient cheap talk communication
Are there any papers about efficient cheap talk communication, where the players achieve the equilibrium payoffs of a correlated strategy as in Aumann's seminal paper? Or in case no such paper exists, ...
6
votes
1answer
55 views
Correlation device that induces a specific transition probability
Taking a look at this paper of Forges and Vida the authors define a correlation device in page $102$, that is a standard probability space $\left(\Omega,\mathcal{B},\mu\right)$, They assume that the ...
4
votes
0answers
47 views
Repeated Games of Incomplete information set up and questions
The following are from the model of Jérôme Renault (Repeated Games of incomplete infomration).
The preliminaries of the model
Formally, a repeated game with incomplete information is given by the ...
1
vote
0answers
30 views
Perfect recall vs perfect monitoring
Following my previous previous post here, I would like to add another question. Is perfect recall the same with perfect monitoring? If not, what are their differences?
0
votes
1answer
34 views
Perfect recall assumption
When we assume that the players can recall perfectly everything about the previous stages of a game, in essence we assume that they know the history path that they followed until they reached to some ...
1
vote
0answers
26 views
Definition of the space of a repeated game
I want to define the space of a stochastic game and it confuses me a lot, so I want someone to check please the space $\Theta$ that I define at the end and how could I define the sigma algebra of this ...
1
vote
0answers
24 views
How to define a dynamic programming problem in an incomplete information game?
How can I define a problem of dynamic programming, to use the Hamilton-Jacobi-Bellman equation in order to solve the utility maximization problem of the generic agent of a dynamic game with incomplete ...
2
votes
0answers
39 views
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 ...
1
vote
1answer
101 views
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' ...
4
votes
1answer
121 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 ...
2
votes
0answers
42 views
Fehr-Schmidt, Ultimatum game, Subgame-Perfect Nash Equilibrium
I'm studying the different variations of the ultimatum games. I've spent some time on this following game:
Assume now that each player does not only care about the amount of money she receives, but ...
2
votes
2answers
161 views
Pure-Strategy Bayesian Nash equilibrium with general common prior
I'm doing a problem set on the subject of Bayesian Nash equilibrium. I'm asked to find the pure-strategy BNE of the following. I've calculated to matrix shown below. My first concern is if I've ...
2
votes
1answer
64 views
Estimation of point-identified Dynamic Discrete Choice models with moment inequalities
I'm trying to understand and implement in code the method in Bajari, Benkard, Levin (2007). The first stage is clear to me, as well as how to forward-simulate to obtain an estimate of the value ...
2
votes
4answers
117 views
How to achieve the best outcome by a single statement in this game?
This game is taken from Schelling's Game Theory: How to Make Decisions by R.V. Dodge, in which contenders practice brinksmanship to their own advantages. It goes as follows:
Anderson, Barnes, and ...
2
votes
1answer
85 views
Sequential Game is Extensive form game?
Dynamic, Sequential, Stochastic, Extensive form and Evolutionary games.
I know what all of them mean very roughly.
I want to clarify them.
As I understand Extensive form is a description of a ...
2
votes
1answer
114 views
Definition of subgame perfect Nash equilibrium
Take a two-stage game with complete information and simultaneous actions in each state:
(1) Player 1 and 2 simultaneously choose action $a_1\in A_1$ and
$a_2\in A_2$ respectively.
(2) Player 1 and ...
5
votes
1answer
222 views
What is the game theory of retaliatory trade tariffs?
Suppose no tariffs, or negligible tariffs, exist between nations A and B, and suddenly A introduces substantive tariffs on certain products A imports from B. In theory, this could lead to B and A ...
0
votes
1answer
188 views
Spence's Job Market Signaling Game
I have a little doubt in the Job Market Signalling Game. I am referring to A Primer in Game Theory: Gibbons, Chapter 4, Signaling Games
The attached paragraph refers to a Separating Equilibrium case ...
2
votes
1answer
162 views
Repeated Game SPNE
I approached this question in this way:
$(P_1,P_2), (R_1,R_2), (S_1,S_2)$ are the Nash Equilibria of the Stage 1 game. For the given strategy to be sustained as SPNE, there should be no way unilateral ...
1
vote
1answer
162 views
SPNE and Pareto Optimality
"The SPNE of a sequential game might not necessarily be Pareto Optimal"
I understand the definitons of Nash Equilibria and Pareto Optimality and that these are not synonymous concepts. An example in ...
-1
votes
1answer
457 views
Sequential Bertrand game with differentiated goods, how to write the strategies of firm 2 [closed]
In a Bertrand competition with differentiated goods where firms set the prices sequentially, we have the following demand functions:
q1 is quantity of goods demanded for firm 1
q2 is quantity of ...
2
votes
0answers
222 views
Subgame Perfect Equilibrium with Pure Strategies in Sequential Games [closed]
If I have a sequential game, i.e. in each node (that I will call $t$) only one player choose an strategy from a finite space of strategies, Is it true there always exist a subgame perfect equilibrium ...
2
votes
2answers
131 views
Price setting firms with cost reduction technology
As part of my undergraduate studies in Industrial Economics, I am trying to solve the following question:
Two price-setting firms are competing in a market for a homogeneous product. There are 10,...
3
votes
1answer
105 views
Extensive Form Games
( The game of “ chicken”) Two cars are driving at each other at great speeds.
If nobody changes directions, in 3 seconds they will collide and die a gruesome death,
yielding payoffs of −100 for both ...
1
vote
1answer
51 views
World as a society of interlinked multiplayer individuals
If you were to take a game-theoretic model of a world in which each individual tried to optimize their utility function / goals then how would you go about designing a computer simulation of the ...
1
vote
0answers
82 views
Dynamic dividing a dollar game
The question is a reformulation of an incomplete version.
Consider the following dynamic dividing a dollar game where agent 1 claims $x(t)$ of the dollar and agent 2 $y(t)$ (paper).
\begin{align}
&...
1
vote
0answers
67 views
Dynamic contract theory: Demarzo, Fishman(2007) optimal long term financial contracting
I am reading Demarzo, Fishman(RFS,2007). Any suggestion will be appreciated. My questions are the following:
(a)
\begin{equation*}
b_T^e(a) = \left\{\begin{array}{lll}
-e^{(\gamma-r)(...
2
votes
1answer
68 views
Terminology for "part" of extensive form game
How should I call a "part" of an extensive form game which is neither (i) a subgame, nor (ii) a stage in a repeated game?
For instance, consider the class of games constructed by "stacking" 2 ...
6
votes
2answers
208 views
Multiple equilibria: which one to select?
There are two agents $i=1,2$. Consider the following programm
\begin{align}
&V_1(x_0) := \max_u \int^\infty_0 e^{-\rho t}F_1(x(t),u(t),v(t))dt\\
&V_2(x_0) := \max_v \int^\infty_0 e^{-\rho t}...
3
votes
0answers
67 views
Converging Trajectories and Sufficiency for Optimality
(The question is loosely relatet to this thread.)
In the paper "Feedback Equilibria for a class of non-linear Differential Games" by Mäler et al. it is stated (p. 14)
In fact sufficiency is ...
5
votes
0answers
102 views
Can repeated bidding in an auction make each player's type common knowledge?
In Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz(2007), there's a hand-waving argument to justify their setting as a game of complete information:
we assume that all values are common
...
7
votes
1answer
119 views
How to verify Value Function in nonzero sum two player Differential Game?
There are two agents $i=1,2$. The state $k$ is governed by $\tau_i\in[0,1]$ where
\begin{align}
\dot{k} = f(k,\tau_1,\tau_2).
\end{align}
Define the value function of player $i$ by
\begin{align}
v_i(...
9
votes
1answer
349 views
What does Battigalli really mean by "Players can not choose strategies, they can only choose actions."?
In this video (from 7: 30 to 9: 00)on Youtube, Battigalli mentions the state of world for a simple three-legged centipede game, which, in his own word, is
"$\ldots$a description of everything ...
5
votes
2answers
141 views
Repeated games without a beginning and an end
I'm interested to know results on repeated games indexing each stage game by $\mathbb Z$ which contrast with those indexed by $\mathbb Z_+$.
It seems to me this could be quite different from repeated ...
7
votes
1answer
249 views
Models for online markets with reputation system
The only relevant model I'm aware of is Liu Qingmin(2011 R.E.S). Is there any other decent models dealing with the mechanism of online markets under reputation system, and perhaps linking to ...
5
votes
2answers
605 views
One-shot deviation principle for infinite repeated games and dynamic programming
In a context that future return is discounted by a constant parameter, one-shot deviation principle holds for both repeated games and dynamic programming.
Because, in repeated games, a one-shot ...
8
votes
1answer
312 views
Identification with BBL
In the last few years, the estimator proposed by Bajari, Benkard, and Levin ('07) for dynamic games has been gaining popularity. It is relatively straight forward and is one of the only viable options ...
