Advertising cooperative phenotype through costly signals facilitates collective action.

Around the world, people engage in practices that involve self-inflicted pain and apparently wasted resources. Researchers theorized that these practices help stabilize within-group cooperation by assorting individuals committed to collective action. While this proposition was previously studied using existing religious practices, we provide a controlled framework for an experimental investigation of various predictions derived from this theory. We recruited 372 university students in the Czech Republic who were randomly assigned into either a high-cost or low-cost condition and then chose to play a public goods game (PGG) either in a group that wastes money to signal commitment to high contributions in the game or to play in the group without such signals. We predicted that cooperators would assort in the high-cost revealed group and that, despite these costs, they would contribute more to the common pool and earn larger individual rewards over five iterations of PGG compared with the concealed group and participants in the low-cost condition. The results showed that the assortment of cooperators was more effective in the high-cost condition and translated into larger contributions of the remaining endowment to the common pool, but participants in the low-cost revealed group earned the most. We conclude that costly signals can serve as an imperfect assorting mechanism, but the size of the costs needs to be carefully balanced with potential benefits to be profitable.

Social decision-making in the brain: Input-state-output modelling reveals patterns of effective connectivity underlying reciprocal choices.

During social interactions, decision-making involves mutual reciprocity-each individual's choices are simultaneously a consequence of, and antecedent to those of their interaction partner. Neuroeconomic research has begun to unveil the brain networks underpinning social decision-making, but we know little about the patterns of neural connectivity within them that give rise to reciprocal choices. To investigate this, the present study measured the behaviour and brain function of pairs of individuals (N = 66) whilst they played multiple rounds of economic exchange comprising an iterated ultimatum game. During these exchanges, both players could attempt to maximise their overall monetary gain by reciprocating their opponent's prior behaviour-they could promote generosity by rewarding it, and/or discourage unfair play through retaliation. By adapting a model of reciprocity from experimental economics, we show that players' choices on each exchange are captured accurately by estimating their expected utility (EU) as a reciprocal reaction to their opponent's prior behaviour. We then demonstrate neural responses that map onto these reciprocal choices in two brain regions implicated in social decision-making: right anterior insula (AI) and anterior/anterior-mid cingulate cortex (aMCC). Finally, with behavioural Dynamic Causal Modelling, we identified player-specific patterns of effective connectivity between these brain regions with which we estimated each player's choices with over 70% accuracy; namely, bidirectional connections between AI and aMCC that are modulated differentially by estimates of EU from our reciprocity model. This input-state-output modelling procedure therefore reveals systematic brain-behaviour relationships associated with the reciprocal choices characterising interactive social decision-making.

A dual-fMRI investigation of the iterated Ultimatum Game reveals that reciprocal behaviour is associated with neural alignment.

Dyadic interactions often involve a dynamic process of mutual reciprocity; to steer a series of exchanges towards a desired outcome, both interactants must adapt their own behaviour according to that of their interaction partner. Understanding the brain processes behind such bidirectional reciprocity is therefore central to social neuroscience, but this requires measurement of both individuals' brains during real-world exchanges. We achieved this by performing functional magnetic resonance imaging (fMRI) on pairs of male individuals simultaneously while they interacted in a modified iterated Ultimatum Game (iUG). In this modification, both players could express their intent and maximise their own monetary gain by reciprocating their partner's behaviour - they could promote generosity through cooperation and/or discourage unfair play with retaliation. By developing a novel model of reciprocity adapted from behavioural economics, we then show that each player's choices can be predicted accurately by estimating expected utility (EU) not only in terms of immediate payoff, but also as a reaction to their opponent's prior behaviour. Finally, for the first time we reveal that brain signals implicated in social decision making are modulated by these estimates of EU, and become correlated more strongly between interacting players who reciprocate one another.

Generating subtour elimination constraints for the TSP from pure integer solutions.

The traveling salesman problem (TSP) is one of the most prominent combinatorial optimization problems. Given a complete graph [Formula: see text] and non-negative distances d for every edge, the TSP asks for a shortest tour through all vertices with respect to the distances d. The method of choice for solving the TSP to optimality is a branch and cut approach. Usually the integrality constraints are relaxed first and all separation processes to identify violated inequalities are done on fractional solutions. In our approach we try to exploit the impressive performance of current ILP-solvers and work only with integer solutions without ever interfering with fractional solutions. We stick to a very simple ILP-model and relax the subtour elimination constraints only. The resulting problem is solved to integer optimality, violated constraints (which are trivial to find) are added and the process is repeated until a feasible solution is found. In order to speed up the algorithm we pursue several attempts to find as many relevant subtours as possible. These attempts are based on the clustering of vertices with additional insights gained from empirical observations and random graph theory. Computational results are performed on test instances taken from the TSPLIB95 and on random Euclidean graphs.