would lead to an uninteresting global “chicken” strategy (all players declaring king until the final seconds of the experiment, with some players then “blinking” and switching to pawn), in these experiments payoffs accrued continuously according to the prorated time players spent in each of the three possible states (pawn, king with no conflicting neighbors, conflicting kings).

Every experiment was run under two conditions—one just as described above, and another in which the GUI included an additional element: in the case that the player was the lone king in their neighborhood, and thus enjoying the highest rate of pay, a slider bar permitted them to specify a fraction of their earnings in that state to be shared equally among all their neighbors (whose pawn status allows the king’s high payoff). These “tips” or side payments could range from 0% to 100% in increments of 10%, and could be adjusted at any time. Note that in some cases, depending on network structure, some vertices might be able to obtain a higher rate of pay by being a pawn receiving side payments from many neighboring kings than by being the lone king in their neighborhood.

The most striking finding was that, across a wide variety of network structures, the introduction of the side payments uniformly raised the collective payoffs or social welfare. Side payment rates were often generous, and averaged close to 20%. Furthermore, when side payments are introduced, both the average income disparity between neighboring players, and the amount of time they spend as conflicting kings, are considerably reduced, across all network structures examined (see Figure 6). This suggests that without side payments, subjects used conflict, which reduces the wealth of all players involved, to express perceived unfairness or inequality. The side payments reduce unfairness and consequently reduce conflict, thus facilitating coordination and raising the social welfare.

Biased voting. The biased voting experiments14 shared with the earlier consensus experiments an incentive toward collective agreement and coordination, but with an important strategic twist. As in consensus, each

the side payments
reduce unfairness
and consequently
reduce conflict,
thus facilitating
coordination
and raising the
social welfare.

player had to simply select a color for their vertex, but now only between the two colors red and blue. If within the allotted time, the entire population converged unanimously to either red or blue, the experiment was halted and every player received some payoff. If this did not occur within the allotted time, every player received nothing for that experiment. Thus the incentives were now not at the individual level, but at the collective—players had to not only agree with their neighbors, but with the entire network, even though they were still given only local views and interactions.

The strategic twist was that different players were paid different amounts for convergence to the two colors within the same experiment. In particular, some players received a higher payoff for convergence to blue, while others received a higher payoff for convergence to red. Typical incentives might pay blue-preferring players $1.50 for blue convergence and only $0.50 for red, with red-preferring players receiving the reverse. Some experiments permitted asymmetries between higher and lower payoffs, thus incentivizing some players to “care” more about the color chosen by the population. These experiments thus set up a deliberate tension between competing individual preferences and the need for collective unity.

In the most dramatic set of experiments, networks were chosen according to preferential attachment— known to generate a small number of vertices with high degree—and the vast majority of players given incentives that paid more for convergence to blue. However, the minority of vertices preferring red was chosen to be the high-degree vertices. These experiments tested whether a small but well-connected minority could systematically impose its preferences on the majority, thus resulting in suboptimal social welfare.

The answer was resoundingly affirmative: in 27 such “minority power” experiments, 24 of them resulted in the subjects reaching a unanimous choice—in every case, the preferred choice of the well-connected minority. The finding is especially surprising when we remember that since everyone has only local views and information,