I just stumbled upon this and noticed that a real-world mechanism for international climate policy cooperation that I recently suggested in this paper can be interpreted as a special case of your (G,X,Y) framework.
Assume a fixed game G where
each player’s action space is the nonnegative reals,
U(x,y) is weakly decreasing in x and weakly increasing in y.
V(x,y) is weakly decreasing in y and weakly increasing in x.
(Many public goods games, such as the Prisoners’ Dilemma, have such a structure)
Let’s call an object a Conditional Commitment Function (CCF) iff it is a bounded, continuous, and weakly increasing function from the nonnegative reals into the nonnegative reals. (Intended interpretation of a CCF C: If opponent agrees to do y, I agree to do any x that has x ⇐ C(y))
Now consider programs of the following kind:
C = <some CCF>
if code(opponent) equals code(myself) except that C is replaced by some CCF D:
output the largest x >= 0 for which there is a y <= D(x) with x <= C(y)
else:
output 0
Let’s denote this program Z(C) , where C is the CCF occurring in line 1 of the program. Finally, let’s consider the meta-game where two programmers A and B, knowing G, each simultaneously choose a C and submit the program Z(C), the two programs are executed once to determine actions (x,y), A gets U(x,y) and B gets V(x,y).
(In the real world, the “programmers” could be the two parliaments of two countries that pass two binding laws (the “programs”), and the actions could be domestic levels of greenhouse gas emissions reductions.)
In our paper, we prove that the outcomes that will result from the strong Nash equilibria of this meta-game are exactly the Pareto-optimal outcomes (x,y) that both programmers prefer to the outcome (0,0).
(In an N (instead of 2) player context, the outcomes of strong Nash equilibria are exactly the ones from a certain version of the underlying base game’s core, a subset of the Pareto frontier that might however be empty).
I’d be interested in learning whether you think this is an interesting application context to explore the theories you discuss.
I just stumbled upon this and noticed that a real-world mechanism for international climate policy cooperation that I recently suggested in this paper can be interpreted as a special case of your (G,X,Y) framework.
Assume a fixed game G where
each player’s action space is the nonnegative reals,
U(x,y) is weakly decreasing in x and weakly increasing in y.
V(x,y) is weakly decreasing in y and weakly increasing in x.
(Many public goods games, such as the Prisoners’ Dilemma, have such a structure)
Let’s call an object a Conditional Commitment Function (CCF) iff it is a bounded, continuous, and weakly increasing function from the nonnegative reals into the nonnegative reals. (Intended interpretation of a CCF C: If opponent agrees to do y, I agree to do any x that has x ⇐ C(y))
Now consider programs of the following kind:
Let’s denote this program Z(C) , where C is the CCF occurring in line 1 of the program. Finally, let’s consider the meta-game where two programmers A and B, knowing G, each simultaneously choose a C and submit the program Z(C), the two programs are executed once to determine actions (x,y), A gets U(x,y) and B gets V(x,y).
(In the real world, the “programmers” could be the two parliaments of two countries that pass two binding laws (the “programs”), and the actions could be domestic levels of greenhouse gas emissions reductions.)
In our paper, we prove that the outcomes that will result from the strong Nash equilibria of this meta-game are exactly the Pareto-optimal outcomes (x,y) that both programmers prefer to the outcome (0,0).
(In an N (instead of 2) player context, the outcomes of strong Nash equilibria are exactly the ones from a certain version of the underlying base game’s core, a subset of the Pareto frontier that might however be empty).
I’d be interested in learning whether you think this is an interesting application context to explore the theories you discuss.