Julian Garcia

Modes of migration and multilevel selection in evolutionary multiplayer games

The evolution of cooperation in group-structured populations has received much attention, but little is known about the effects of different modes of migration of individuals between groups. Here, we have incorporated four different modes of migration that differ in the degree of coordination among the individuals. For each mode of migration, we identify the set of multiplayer games in which the cooperative strategy has higher fixation probability than defection. The comparison shows that the set of games under which cooperation may evolve generally expands depending upon the degree of coordination among the migrating individuals. Weak altruism can evolve under all modes of individual migration, provided that the benefit to cost ratio is high enough. Strong altruism, however, evolves only if the mode of migration involves coordination of individual actions. Depending upon the migration frequency and degree of coordination among individuals, conditions that allow selection to work at the level of groups can be established.

A computational model of task allocation in social insects: ecology and interactions alone can drive specialisation

Social insect colonies are capable of allocating their workforce in a decentralised fashion; addressing a variety of tasks and responding effectively to changes in the environment. This process is fundamental to their eco-logical success, but the mechanisms behind it remain poorly understood. While most models focus on internal and individual factors, empirical evidence highlights the importance of ecology and social interactions. To address this gap we propose a game theoretical model of task allocation. Individuals are characterised by a trait that determines how they split their energy between the two prototypical tasks of foraging and regulation. A viable colony needs to learn to adequately split their energy between the two tasks. We study two different social processes: individuals can learn to play this game by relying exclusively on their own experience, or by relying on the experiences of others via social learning. A computational model allows for direct manipulation of individual interactions and ecology. We find that social organisation can be completely determined by the ecology alone: irrespective of interaction details, weakly specialised colonies in which all individuals tend to both tasks emerge when foraging is cheap; harsher environments, on the other hand, lead to strongly specialised colonies in which each individual fully engages in a single tasks. We compare the outcomes of self-organised task allocation with optimal group performance. Counter to intuition, strongly specialised colonies perform suboptimally, whereas the group performance of weakly specialised colonies is closer to optimal. Differences in social interactions are salient when the colony deals with dynamic environments. Colonies whose individuals rely on their own experience are better able to deal with change. Our computational model is aligned with mathematical predictions in tractable limits. We believe this different kind of model is useful in framing relevant and important empirical questions.

No Strategy Can Win in the Repeated Prisoner's Dilemma: Linking Game Theory and Computer Simulations

Computer simulations are regularly used for studying the evolution of strategies in repeated games. These simulations rarely pay attention to game theoretical results that can illuminate the data analysis or the questions being asked. Results from evolutionary game theory imply that for every Nash equilibrium, there are sequences of mutants that would destabilize them. If strategies are not limited to a finite set, populations move between a variety of Nash equilibria with different levels of cooperation. This instability is inescapable, regardless of how strategies are represented. We present algorithms that show that simulations do agree with the theory. This implies that cognition itself may only have limited impact on the cycling dynamics. We argue that the role of mutations or exploration is more important in determining levels of cooperation.

Incentive Compatibility of Pay Per Last N Shares in Bitcoin Mining Pools

Pay per last N shares (PPLNS) is a popular pool mining reward mechanism on a number of cryptocurrencies, including Bitcoin. In PPLNS pools, miners may stand to benefit by delaying reports of found shares. This attack may entail unfair or inefficient outcomes. We propose a simple but general game theoretical model of delays in PPLNS. We derive conditions for incentive compatible rewards, showing that the power of the most powerful miner determines whether incentives are compatible or not. An efficient algorithm to find Nash equilibria is put forward, and used to show how fairness and efficiency deteriorate with inside-pool inequality. In pools where all players have comparable computational power incentives to deviate from protocol are minor, but gains may be considerable in pools where miner’s resources are unequal. We explore how our findings can be applied to ameliorate delay attacks by fitting real-world parameters to our model.

The Nature of Nature: Why Nature-Inspired Algorithms Work

Nature has inspired many algorithms for solving complex problems. Understanding how and why these natural models work leads not only to new insights about nature, but also to an understanding of deep relationships between familiar algorithms. Here, we show that network properties underlie and define a whole family of nature-inspired algorithms. In particular, the network defined by neighbourhoods within landscapes (real or virtual) underlies the searches and phase transitions mediate between local and global search. Three paradigms drawn from computer science—dual-phase evolution, evolutionary dynamics and generalized local search machines—provide theoretical foundations for understanding how nature-inspired algorithms function. Several algorithms provide useful examples, especially genetic algorithms, ant colony optimization and simulated annealing.