Post by Christian Hilbe

Yesterday, two papers got published in PNAS (https://www.pnas.org) to which I contributed to. Both papers deal with strategic behavior in repeated games. But otherwise, they are quite different: https://lnkd.in/dvKPABPF https://lnkd.in/dchYuwN3 Here's a quick summary: The first paper with Philip LaPorte, Nikoleta E. Glynatsi and Martin Nowak asks an important theoretical question. Repeated games allow for (uncountably) many strategies. To facilitate an analysis, researchers often study simplified subspaces. To which extent are such results reliable? The question is this: if some strategy p is superior in a restricted space S, how would we know whether this strategy would still perform well if we allowed for more complex strategies? To address this question, Philip introduces two notions of "complete strategy spaces". A space S is "best reply complete" if any strategy p in S has a best reply in S. The space is "payoff complete" if any payoff achievable against p (with an arbitrary strategy) can be realized with a strategy in S. Both notions address whether strategies outside S can outperform strategies within S. In the paper, Philip gives an elegant (sufficient) condition for strategy spaces to be both best reply complete and payoff complete. His result builds on important previous work by Levinski et al, https://lnkd.in/dsAcjZGw The second paper, with Xiaomin Wang and Boyu Zhang focuses on an empirical question: to which extent do different asymmetries between players affect their ability to cooperate and coordinate?  To explore this question, Xiaomin studied a large sample of participants (N>1,500) to explore contributions in public good games. We varied group size, endowments, productivities, and whether the public goods game is linear or non-linear (threshold game).  For linear games, we find that certain forms of inequality can be advantageous: the largest surplus is achieved when more productive participants receive larger endowments. This confirms previous results among western online participants, https://lnkd.in/dkStKG65 However, for nonlinear games, we find that any form of (endowment) inequality is detrimental, because it renders successful coordination more difficult. I personally learned a lot from both projects; the first authors have put a lot of work into them (of course, all other authors too 😀).