Cost-efficient interventions for promoting fairness in the ultimatum game

Evolution of trust in N-player trust games with loss assessment

Trust plays a crucial role in social and economic interactions, serving as the foundation for social stability and human cooperation. Previous studies have explored the evolution of trust between investors and trustees by constructing trust game models, incorporating factors such as network structure, reputation, and incentives. However, these studies often assume that investors consistently maintain their investment behavior, neglecting the potential influence of the investment environment on investment behavior. To address this gap, we introduce a loss assessment mechanism and construct a trust game model. Specifically, investors first allocate their investment amount to an assessment agency, which divides the amount into two parts according to a certain allocation ratio. One part is used for investment assessment, and the results are fed back to the investors. If the payoff from this portion exceeds the investors' expected value, the remaining amount is invested; otherwise, it is returned to the investors. The results indicate that investors with moderate expectations are more likely to form alliances with trustworthy trustees, thereby effectively promoting the evolution of trust. Conversely, lower or higher expectations yield opposite results. Additionally, we find that as investors' expected values increase, the corresponding allocation ratio should also increase to achieve higher payoffs.

Cost Optimisation of Individual-Based Institutional Reward Incentives for Promoting Cooperation in Finite Populations

In this paper, we study the problem of cost optimisation of individual-based institutional incentives (reward, punishment, and hybrid) for guaranteeing a certain minimal level of cooperative behaviour in a well-mixed, finite population. In this scheme, the individuals in the population interact via cooperation dilemmas (Donation Game or Public Goods Game) in which institutional reward is carried out only if cooperation is not abundant enough (i.e., the number of cooperators is below a threshold 1 ≤ t ≤ N - 1 , where N is the population size); and similarly, institutional punishment is carried out only when defection is too abundant. We study analytically the cases t = 1 for the reward incentive under the small mutation limit assumption and two different initial states, showing that the cost function is always non-decreasing. We derive the neutral drift and strong selection limits when the intensity of selection tends to zero and infinity, respectively. We numerically investigate the problem for other values of t and for population dynamics with arbitrary mutation rates.

Cost optimisation of hybrid institutional incentives for promoting cooperation in finite populations

In this paper, we rigorously study the problem of cost optimisation of hybrid (mixed) institutional incentives, which are a plan of actions involving the use of reward and punishment by an external decision-maker, for maximising the level (or guaranteeing at least a certain level) of cooperative behaviour in a well-mixed, finite population of self-regarding individuals who interact via cooperation dilemmas (Donation Game or Public Goods Game). We show that a mixed incentive scheme can offer a more cost-efficient approach for providing incentives while ensuring the same level or standard of cooperation in the long-run. We establish the asymptotic behaviour (namely neutral drift, strong selection, and infinite-population limits). We prove the existence of a phase transition, obtaining the critical threshold of the strength of selection at which the monotonicity of the cost function changes and providing an algorithm for finding the optimal value of the individual incentive cost. Our analytical results are illustrated with numerical investigations. Overall, our analysis provides novel theoretical insights into the design of cost-efficient institutional incentive mechanisms for promoting the evolution of cooperation in stochastic systems.

Does Spending More Always Ensure Higher Cooperation? An Analysis of Institutional Incentives on Heterogeneous Networks

Humans have developed considerable machinery used at scale to create policies and to distribute incentives, yet we are forever seeking ways in which to improve upon these, our institutions. Especially when funding is limited, it is imperative to optimise spending without sacrificing positive outcomes, a challenge which has often been approached within several areas of social, life and engineering sciences. These studies often neglect the availability of information, cost restraints or the underlying complex network structures, which define real-world populations. Here, we have extended these models, including the aforementioned concerns, but also tested the robustness of their findings to stochastic social learning paradigms. Akin to real-world decisions on how best to distribute endowments, we study several incentive schemes, which consider information about the overall population, local neighbourhoods or the level of influence which a cooperative node has in the network, selectively rewarding cooperative behaviour if certain criteria are met. Following a transition towards a more realistic network setting and stochastic behavioural update rule, we found that carelessly promoting cooperators can often lead to their downfall in socially diverse settings. These emergent cyclic patterns not only damage cooperation, but also decimate the budgets of external investors. Our findings highlight the complexity of designing effective and cogent investment policies in socially diverse populations.

Optimization of institutional incentives for cooperation in structured populations

The application of incentives, such as reward and punishment, is a frequently applied way for promoting cooperation among interacting individuals in structured populations. However, how to properly use the incentives is still a challenging problem for incentive-providing institutions. In particular, since the implementation of incentive is costly, to explore the optimal incentive protocol, which ensures the desired collective goal at a minimal cost, is worthy of study. In this work, we consider the positive and negative incentives for a structured population of individuals whose conflicting interactions are characterized by a Prisoner's Dilemma game. We establish an index function for quantifying the cumulative cost during the process of incentive implementation, and theoretically derive the optimal positive and negative incentive protocols for cooperation on regular networks. We find that both types of optimal incentive protocols are identical and time-invariant. Moreover, we compare the optimal rewarding and punishing schemes concerning implementation cost and provide a rigorous basis for the usage of incentives in the game-theoretical framework. We further perform computer simulations to support our theoretical results and explore their robustness for different types of population structures, including regular, random, small-world and scale-free networks.

Evolution of cooperation under a generalized death-birth process

According to the evolutionary death-birth protocol, a player is chosen randomly to die and neighbors compete for the available position proportional to their fitness. Hence, the status of the focal player is completely ignored and has no impact on the strategy update. In this paper, we revisit and generalize this rule by introducing a weight factor to compare the payoff values of the focal and invading neighbors. By means of evolutionary graph theory, we analyze the model on joint transitive graphs to explore the possible consequences of the presence of a weight factor. We find that focal weight always hinders cooperation under weak selection strength. Surprisingly, the results show a nontrivial tipping point of the weight factor where the threshold of cooperation success shifts from positive to negative infinity. Once focal weight exceeds this tipping point, cooperation becomes unreachable. Our theoretical predictions are confirmed by Monte Carlo simulations on a square lattice of different sizes. We also verify the robustness of the conclusions to arbitrary two-player prisoner's dilemmas, to dispersal graphs with arbitrary edge weights, and to interaction and dispersal graphs overlapping arbitrarily.

Emergent behaviours in multi-agent systems with Evolutionary Game Theory

The mechanisms of emergence and evolution of collective behaviours in dynamical Multi-Agent Systems (MAS) of multiple interacting agents, with diverse behavioral strategies in co-presence, have been undergoing mathematical study via Evolutionary Game Theory (EGT). Their systematic study also resorts to agent-based modelling and simulation (ABM) techniques, thus enabling the study of aforesaid mechanisms under a variety of conditions, parameters, and alternative virtual games. This paper summarises some main research directions and challenges tackled in our group, using methods from EGT and ABM. These range from the introduction of cognitive and emotional mechanisms into agents’ implementation in an evolving MAS, to the cost-efficient interference for promoting prosocial behaviours in complex networks, to the regulation and governance of AI safety development ecology, and to the equilibrium analysis of random evolutionary multi-player games. This brief aims to sensitize the reader to EGT based issues, results and prospects, which are accruing in importance for the modeling of minds with machines and the engineering of prosocial behaviours in dynamical MAS, with impact on our understanding of the emergence and stability of collective behaviours. In all cases, important open problems in MAS research as viewed or prioritised by the group are described.

Costly incentives design from an institutional perspective: cooperation, sustainability and affluence

Incentives are usually introduced by the regulator entity (third-party), to promote cooperation in a market. The implementation of incentives is always costly and thus might fail to be enforced sustainably. This work aims at exploring the effects of incentives from an institutional perspective, while coping with the scenario where the third-party is part of the system but not composed by players. The evolutionary game theory (EGT) framework is applied to identify the incentives that lead to pure cooperation. In contrast to traditional EGT, this paper introduces an elimination mechanism that can reduce the market size. The incentives identified in the EGT analysis are further examined in simulation experiments which measure the market size, affluence and sustainability. The findings show: (1) light punishment leads to a reduction of the market size, yet heavier punishment is beneficial to the market size and wealth; (2) mixed incentives will generally lead to different wealth of the third party and of the participants. While under moderate strength, the wealth of both parties is the same and their overall wealth is maximal; (3) for sustainability, pure punishment (resp. reward) is sustainable (resp. unsustainable), the sustainability of mixed incentives depends on both their strength and agents’ rationality level.

Institutional incentives for the evolution of committed cooperation: ensuring participation is as important as enhancing compliance

Both conventional wisdom and empirical evidence suggest that arranging a prior commitment or agreement before an interaction takes place enhances the chance of reaching mutual cooperation. Yet it is not clear what mechanisms might underlie the participation in and compliance with such a commitment, especially when participation is costly and non-compliance can be profitable. Here, we develop a theory of participation and compliance with respect to an explicit commitment formation process and to institutional incentives where individuals, at first, decide whether or not to join a cooperative agreement to play a one-shot social dilemma game. Using a mathematical model, we determine whether and when participating in a costly commitment, and complying with it, is an evolutionarily stable strategy, resulting in high levels of cooperation. We show that, given a sufficient budget for providing incentives, rewarding of commitment compliant behaviours better promotes cooperation than punishment of non-compliant ones. Moreover, by sparing part of this budget for rewarding those willing to participate in a commitment, the overall level of cooperation can be significantly enhanced for both reward and punishment. Finally, the presence of mistakes in deciding to participate favours evolutionary stability of commitment compliance and cooperation.

Artificial intelligence development races in heterogeneous settings

Regulation of advanced technologies such as Artificial Intelligence (AI) has become increasingly important, given the associated risks and apparent ethical issues. With the great benefits promised from being able to first supply such technologies, safety precautions and societal consequences might be ignored or shortchanged in exchange for speeding up the development, therefore engendering a racing narrative among the developers. Starting from a game-theoretical model describing an idealised technology race in a fully connected world of players, here we investigate how different interaction structures among race participants can alter collective choices and requirements for regulatory actions. Our findings indicate that, when participants portray a strong diversity in terms of connections and peer-influence (e.g., when scale-free networks shape interactions among parties), the conflicts that exist in homogeneous settings are significantly reduced, thereby lessening the need for regulatory actions. Furthermore, our results suggest that technology governance and regulation may profit from the world's patent heterogeneity and inequality among firms and nations, so as to enable the design and implementation of meticulous interventions on a minority of participants, which is capable of influencing an entire population towards an ethical and sustainable use of advanced technologies.