7
Let $N=2$ and for $(x,y)$ and $(p,q)$ in $[0,1]^2$ let $d_{p,q}(x,y)$ be the Euclidean distance between $(p,q)$ and $(x,y)$, i.e. $d_{p,q}(x,y)=[(p-x)^2+(q-y)^2]^{1/2}$.
Choose $k>0$ such that $k<a-b$ and $k<b$.
Now define
$$u(p,q):=\max\{ -d_{p,q}(a,a),-d_{p,q}(b,b),k-d_{p,q}(b,0),k-d_{p,q}(0,b) \}.$$
This function is continuous as a maximum of ...
6
I think the right paper here is Jehiel, Meyer-ter-Vehn, Moldovanu and Zame (Econometrica 2006): The Limits of ex post Implementation.
Take a direct mechanism. Ex post incentive compatibility (EPIC) means that for every realization of all other agents’ types, each agent finds it optimal to report his type truthfully given the others are truthful.
This is ...
6
In Def. 3 of the paper you link to, EPIC is not "defined as truth-telling is the best strategy no matter what the others do". What the $-i$-agents report is held fixed at $\theta_{-i}$, i.e. it is assumed that the others report truthfully.
4
There is another way to compute the symmetric BNE in increasing strategy.
Let $U(v)$ denote the expected utility of a player in equilibrium when his type is $v$: Given that the bidding strategy is increasing, a player with type $0$ will get the good with probability zero.
Thus he/she must bid zero and $U(0) = 0$. For any other $v > 0$, the probability ...
3
If you have in mind infinite populations I'd suggest Carlos Alós-Ferrer (1999) Dynamical Systems with a Continuum of Randomly Matched Agents, Journal of Economic Theory 86 (2), 245-267.
3
Almost all textbooks on game theory include a part on cooperative game theory and therefore also treat Nash bargaining. A random sample ($n=3$) from my shelf produced this one, this one, and this one.
2
We cannot judge if your answer is correct because we don't see the game tree.
First, I would not say that "we can rule out this equlibrium as a possible pooling PBE by the intuitive criterion" because the intuitive criterion is simply a refinement. The PBE is still an equilibrium - it's just that we can say that it appears "unreasonable" ...
2
Think about the incentives of player $i$: If he knew that no one else helps, he'd want to help. If he knew that at least one other player helps, he'd rather not help. A single player helping would make everyone happy, but no one wants to be that single player, because it's costly to help. This is the classical problem of finding a volunteer, so that's why ...
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