Equity dynamics in bargaining without information exchange

Abstract

In this paper, completely uncoupled dynamics for n-player bargaining are proposed that mirror key behavioral elements of early bargaining and aspiration adjustment models (Zeuthen 1930, Sauermann & Selten 1962. Individual adjustment dynamics are based on directional learning adjustments, solely driven by histories of own realized payoffs. Bargaining this way, all possible splits have positive probability in the stationary distribution of the process, but players will split the pie almost equally most of the time. The expected waiting time for almost equal splits to be played is quadratic.JEL classifications: C71, C73, C78, D83

Uncoupled Aspiration Adaptation Dynamics Into the Core

“…Applied to cooperative games, the key property of these dynamics is for coalitions to rearrange if they make some players better‐off (and noone worse off), which dynamically mirrors the ‘blocking argument’ of the core counterfactual. We have studied dynamics that are similar to the ones we consider here in a series of related papers (Nax, ; Nax, ; Nax and Pradelski, ; Nax and Pradelski, ) . In these papers, it is shown that these dynamics implement the core and select equitable core outcomes within the core (of assignment games Nax and Pradelski (), of many‐to‐one matching Nax and Pradelski (), and of multi‐player bargaining Nax ()).…”

“…We have studied dynamics that are similar to the ones we consider here in a series of related papers (Nax, ; Nax, ; Nax and Pradelski, ; Nax and Pradelski, ) . In these papers, it is shown that these dynamics implement the core and select equitable core outcomes within the core (of assignment games Nax and Pradelski (), of many‐to‐one matching Nax and Pradelski (), and of multi‐player bargaining Nax ()). The contribution of this note is to study core implementation for general, superadditive transferable‐utility cooperative games in characteristic function form.…”

“…10. See also Nax (2015) and Nax and Pradelski (2016). grand coalition does not form, it will be convenient to denote by (q S , / S ) the outcome played within coalition S ⊂ N such that S 2 q.)…”

The importance of memory for price discovery in decentralized markets

“…3 In particular, Nax and Pradelski (2015) use a learning rule based on aspiration adaptation (Sauermann and Selten, 1962;Selten, 1998) which found extensive support in laboratory experiments (Tietz and Weber, 1972;Tietz et al, 1978;Scholz et al, 1983). Aspiration-based learning rules were subsequently used by Nax (2015), Pradelski (2015), and Hamza and Shamma (2017) and form the basis for our proposed effectively convergent dynamic.…”

Selection of the distributional rule as an alternative tool to foster cooperation in a Public Good Game

“…not in every case we observe that the larger the group, the lower the contribution. Finally, there are also some works that explain the level of contribution as a reinforcement learning process (Nax and Perc (2015), Nax (2015)). For an exhaustive review on the different elements that are able to influence the contribution to the public good see Perc et al (2013).…”