Subgame Perfect Nash Equilibrium: A Learning Approach via Costs to Move

Caruso, Francesco; Ceparano, Maria Carmela; Morgan, Jacqueline

doi:10.1007/s13235-018-0277-3

Cited by 9 publications

(11 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Suffice it to say that, for finite-action games, fictitious play may offer insights (Brown 1951;Fudenberg and Levine 1994;Robinson 1951;Shapley 1964). For games with continuous actions spaces, see the proximal point procedures in Caruso et al (2018).…”

Section: Proof Player 1 Chooses X Kmentioning

confidence: 99%

Games and cost of change

Flåm

2020

Ann Oper Res

View full text Add to dashboard Cite

Most microeconomic and game theoretic models of individual choice overlook adjustment costs. Rather often, the modeler's concern is just with improvement of objectives. This optic doesn't quite fit agents somewhat tied to status quo. If rational, any such agent reasons whether moving to another state be worth his while. For that, the realized gains must outweigh the inconveniences of the move. Choosing games as chief setting, this paper offers some observations as to the fact that strategy change usually entails cost.

show abstract

Section: Proof Player 1 Chooses X Kmentioning

confidence: 99%

Games and cost of change

Flåm

2020

Ann Oper Res

View full text Add to dashboard Cite

show abstract

“…Therefore, it would be desirable to design constructive methods in order to select an SPNE with the following features: relieving the leader of knowing M , allowing to overcome the diculties deriving from the possible non-single-valuedness of M , providing some behavioural motivations of the players (dierent from the extreme situations described above). Results in this direction have been rst obtained in [93], where an SPNE selection method based on Tikhonov regularization is proposed, and more recently in [22], where proximal regularization is employed.…”

Section: E Subgame Perfect Nash Equilibrium Problemmentioning

confidence: 99%

“…For these reasons and possibly also for behavioural motivations (see, for example, [22]), regularization methods involving the follower's payo function have been introduced. Such methods allow to construct sequences of perturbed problems where the solution of the second-stage problem is unique by exploiting well-known regularization techniques in convex optimization.…”

Section: Regularizing the Follower's Payo Function In Stackelberg Gamesmentioning

confidence: 99%

“…Concerning the second question, the limit of the sequence generated by the solutions to (SP ) P γn for any n ∈ N has no connections, in general, either with weak Stackelberg (or pessimistic) solutions to (P B) or with strong Stackelberg (or optimistic) solutions to (OB), as illustrated in the following example also used in [22].…”

Section: Proximal Regularization Of the Follower's Payo Function In Stackelberg Gamesmentioning

confidence: 99%

See 1 more Smart Citation

Regularization and Approximation Methods in Stackelberg Games and Bilevel Optimization

Caruso

Lignola

Morgan

2020

Bilevel Optimization

Self Cite

View full text Add to dashboard Cite

In a two-stage Stackelberg game, depending on the leader's information about the choice of the follower among his optimal responses, one can associate different types of mathematical problems. We present formulations and solution concepts for such problems, together with their possible connections in bilevel optimization, and we illustrate the crucial issues concerning these solution concepts. Then, we discuss which of these issues can be positively or negatively answered and how managing the latter ones by means of two widely used approaches: regularizing the set of optimal responses of the follower, via different types of approximate solutions, or regularizing the follower's payoff function, via the Tikhonov or the proximal regularizations. The first approach allows to obviate the lack of existence and/or stability through approximating problems, whose solutions exist under not restrictive conditions and enable to construct a surrogate solution to the original problem. The second approach permits to overcome the non-uniqueness of the follower's optimal response, by constructing sequences of Stackelberg games with a unique second-stage solution which approximate in some sense the original game, and to select among the solutions by using a constructive method with behavioural motivations.

show abstract

“…These questions go beyond the scope of this paper. Su¢ ce it to say that, for …nite-action games, …ctitious play may o¤er insights [4], [20], [23]; for games with continuous actions spaces, see the proximal point procedures in [5].…”

mentioning

confidence: 99%

On Games and Cost of Change

Flåm¹

2018

Preprint

View full text Add to dashboard Cite

Many mathematical models of strategic play or better choice overlook adjustment costs. Rather often, the modeler's concern is just with improvement of objectives. This optic doesn't quite fit agents somewhat attached to status quo. They reason whether moving to another state be worth their while. For that, the realized gains must outweigh the inconveniences of the move. This note offers some observations on the fact that change usually entails cost.

show abstract

Subgame Perfect Nash Equilibrium: A Learning Approach via Costs to Move

Cited by 9 publications

References 33 publications

Games and cost of change

Games and cost of change

Regularization and Approximation Methods in Stackelberg Games and Bilevel Optimization

On Games and Cost of Change

Contact Info

Product

Resources

About