BIOEE1610 Game Theory

It is the manner in which an organism interacts with members of its own species, its environment, and members of other species.

• Mechanism: What internal and external factors trigger a given behavior? (how, proximal)
• Ontogeny: How does this behavior develop over the lifespan of the individual? (how, proximal)
• Adaptive value: Why is this behavior adaptive for the individual? (why, causal)
• Phylogeny: How has this behavior evolved over time and why does it differ among species? (why, causal)

Decisions could be conscious or unconscious. Conscious choice is not assumed to be a part of the decision making process.

When animals repeatedly venture out from a central place and then return to consume or cache their food.

This asserts that evolution has favored behaviors that maximize an individuals’s food harvest / intake. This is a part of the optimality theory.

Optimality theory asserts that evolution has favored behaviors that are, in some way, optimal. Usually, optimal strategies are those that maximize the difference between benefits and costs. Included in the evaluation are the organism’s decisions, the currency of the benefits and the costs and any limiting constraints. This can be applied to a wide range of behavior (such as mating, foraging, movement).

Because ideally we must also identify the likelihood of the offspring surviving to reproduce as well. To estimate fitness more easily, we investigate certain currencies instead as proxies, since they’re well correlated with fitness anyway. Additionally, we often work with relative fitness instead of absolute fitness for easier comparison.

• A trait that is expected to be correlated with the fitness of the organism. This could be
• Attributes of the organism itself (body mass etc.)
• Potential reproductive output (mating opportunities or copulations)
• Or it may be a behavior that correlates well with reproductive success (such as food foraging rate)

Running the animal on treadmills in respiration chambers. Alternatively, you can use the mathematical equation connecting body size and running speed with energy consumption.

• Term coined by evolutionary ecologist Joel Brown.
• States that the risk of being killed is a significant cost of foraging (in addition to energy losses due to movement)
• Based on the notion that predators not only reduce prey fitness, but also change their physiology and behavior, which has an impact on fitness.
• Optimal foragers will act accordingly and reduce foraging efforts based on their perceived risk of predation, due to both indirect (environmental changes) and direct (more predators based on the perception of the animal) increases of risk.
• Giving up density is the amount of food that’s left due to the perception of predation risk.
• Not applicable in cities based on bird analysis. Why? (not universally relevant)

Payoff is the fitness yield expected from one strategy against another. Represents the average benefits and costs. Individuals with higher scores should produce more offspring and consequently, their behavioral phenotype should be represented more frequently in subsequent populations.

• It is a strategy (trait behavior) that, when adopted by all members of a population, cannot be successfully invaded by an individual with another strategy. These can either be pure or mixed.
• Mixed: mixed strategies (playing hawk 50% of the time etc) This occurs when the end result is a stable mix of Doves and Hawks. The average fitness of all players, regardless of the strategy they’re playing, is equal. In a mixed ESS, all strategies have an equal average fitness.
• Pure: only one strategy used at given conditions. This occurs when a strategy provides a higher payoff regardless of what the opponent plays.

In game theory, this is when an individual adopts a strategy based on environmental conditions. This is not the same as having a mixed strategy.

This is when the fitness of a phenotype depends on its relative abundance in a population. This is especially important in game theory, where interactions between different strategies depend on the number of individuals with that strategy in the population. The strength of the frequency based selection depends on the game’s costs and benefits.

Cooperation occurs when an actor behaves in a manner that benefits both the recipient and improves the actor’s inclusive fitness. Cooperation includes acts of benefit that may seem altruistic but are actually influenced by kin selection or reciprocity.

This is the sum of the individual’s direct and indirect fitness.

This is fitness derived from the organism’s own reproduction.

Indirect fitness is the fitness received by an individual by helping non descendant kin. Indirect fitness is bolstered by offering assistance that either improves the survival of these relatives or helps them raise their offspring.

• The evolutionary process where traits are favored because they increase the fitness of related individuals. The occurrence of kin selection is predicted by Hamilton’s Rule, which states:
• R (coefficient of relatedness / shared proportion of genome) * Benefit (benefit to the kin ) - cost (cost to the actor) > 0

This is a leading hypothesis in the evolution of cooperation, based on the notion that individuals will repeatedly have the chance to give and receive help.

• Mutual Benefit(+,+): Pack hunting, penguin preserving heat
• Selfishness(-,+): very common in ecology as it’s favored, optimality models assume selfishness
• Altruism (-,+): eusocial species (division of labor, reproduction, common care of offspring - bees, ants etc.)
• Spite (-,-): seen only in humans and social insects?

This hypothesis states that individuals will partake in altruistic behavior when such actions benefit the group as a whole. This hypothesis has been thoroughly debunked, as individuals who “cheat” tend to outcompete altruistic individuals, which would eventually lead to the extinction of altruistic individuals.

In the case of repeated encounters, tit-for-tat seems to work well. For cooperation to evolve, individuals must interact repeatedly and remember some aspects of prior interactions.

• Animals should forage such that they gain the most calories per unit time to maximize their fitness (certain constraints apply)
• There are many different optimal foraging strategies/ models/ measures.
• This, however, is one of the most common measures of optimal foraging.
• When considering optimal foraging, we must consider both costs and benefits. (For example, as the costs of foraging outweigh its benefits in winter, animals hibernate.)
• Energy gain / time decreases linearly due to the depletion of resources.
• Animals stop foraging when energy gain/time is 0 and benefits = costs.
• Many organisms also face a fundamental trade-off between food and safety. Thus, energy rate maximizers must also consider predation within their optimal foraging strategy.

• If you’re desperate, you go get food no matter what.
• Forage in the patch with the greatest return.
• Eat the prey item that has the most calories.
• Quit foraging when the costs = benefits
• Forage in the location with the fewest competitors.

The relative costs and benefits of a given strategy. Influenced by what others do and how frequently they do it. Payoffs are generally highest when the strategy employed is the rarest.

• Optimality theory doesn’t account for the uncertain actions of the others in determining the fitness value of a given behavior.
• Game theory offers a framework to predict fitness values when the actions of others matter.

• It is a theory that states that when individual interests prevail, common resources are likely to be overexploited. Individuals benefit by using more of the resource, so there’s no incentive to not use as much as they can.
• Elinor Ostrom argued that basic game theory and the tragedy of the commons is an oversimplification for humans.
• Truth is important and individuals aren’t trapped by greed.
• Chronicled numerous examples of community success in overcoming the tragedy of the commons.