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npub1ncxn...29r0 7 months ago
In the video I found linked in @RedTailHawk profile mentions the serpent and the dove. I would like to describe the mathematics of this relationship in a copy/paste form from a chatbot. Please excuse my presumptions about the symbolic references I know nothing about. The Hawk-Dove game is a classic example in game theory that models conflict and cooperation between individuals. It illustrates how two strategies—Hawk and Dove—can lead to different outcomes based on the interactions between players. Here’s a breakdown of the mathematical aspects of the game: ### Players and Strategies - **Players**: Two individuals (or animals) interact with each other. - **Strategies**: Each player can choose to be either a Hawk or a Dove. - **Hawk**: Aggressive strategy that fights for resources. - **Dove**: Peaceful strategy that avoids conflict and shares resources. ### Payoff Matrix The outcomes of the interactions are represented in a payoff matrix, which shows the payoffs for each combination of strategies: | | Dove (D) | Hawk (H) | |---------------|----------|----------| | **Dove (D)** | (V/2, V/2) | (0, V) | | **Hawk (H)** | (V, 0) | (R/2, R/2) | ### Payoff Explanation - **V**: Value of the resource being contested. - **R**: Cost of injury from fighting. - **Payoffs**: - If both players choose Dove, they share the resource, resulting in a payoff of \( V/2 \) for each. - If one player is a Hawk and the other is a Dove, the Hawk gets the entire resource (payoff \( V \)), while the Dove gets nothing (payoff \( 0 \)). - If both players are Hawks, they fight, and each incurs a cost from the injury, resulting in a payoff of \( R/2 \) for each. ### Evolutionary Stable Strategy (ESS) In evolutionary terms, the Hawk-Dove game can lead to the concept of an Evolutionary Stable Strategy (ESS). An ESS is a strategy that, if adopted by a population, cannot be invaded by any alternative strategy. 1. **Mixed Strategy Equilibrium**: In some cases, a mixed strategy equilibrium can occur where a certain proportion of the population plays Hawk and the rest plays Dove. The equilibrium can be calculated using the expected payoffs for each strategy. 2. **Equilibrium Condition**: The proportion of Hawks \( p \) and Doves \( 1-p \) can be determined by setting the expected payoffs equal for both strategies. ### Conclusion The Hawk-Dove game illustrates the balance between aggression and cooperation in evolutionary biology and economics. The mathematical framework helps to analyze the strategies and predict the behavior of individuals in competitive situations.

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RedTailHawk redtailhawk@nostrplebs.com 7 months ago
This seems like it maps well onto the Prisoner's Dilemma. I like the Punnett Square analysis technique. I use that to think through lots of stuff besides genetics too. As I think through this, I find myself wanting to convert it to a "cost/benefit" analysis and in each interaction we can either "get along and share equally" or we can "fight it out and winner take all". It would be the same Punnett Square analysis except you'd have both V and R in each quadrant. In 3 of the 4 quadrants, R is 0 for both parties. Likewise, in 3 of the 4 quadrants, V is 100% to the victor. Given those "outcome sets" for those variables, I think it makes most sense to do cost as the numerator (R) and benefit as the denominator (V). In the 3 Dove quadrants, you'd have Cost/Benefit ratios of 0. In the Hawk v Hawk quadrant, if R is the total "damage" from the fight, the "winner Hawk" will have a Cost of somewhere between 0 and R/2 whereas the "loser Hawk" will have a Cost of somewhere between R/2 and R. Winner Hawk will get V and loser Hawk will get 0. Arguably Hawk v Dove is just an edge case of Hawk v Hawk in which the fight is over instantaneously. Likewise, every Hawk v Hawk devolves eventually into Hawk v Dove when a victor is decided. Spiritually speaking, the person acting in accordance with Divine traits would be so apparently powerful that no one would "choose" Hawk mode when interacting with you, while also having the mercy to split the value of the resources with people who are less powerful than you. On the Tree of Life in Kabbalah, this would essentially be the embodiment, balancing, and merger of Geburah (Severity aka Power) and Chesed (Mercy). In the context of cosmological symbolism, hawk, dove, eagle, feathered serpent, dragon...they all are pointing at flight in an homage to the "feather of Ma'at" from Egypt. If your soul was LIGHTer than a feather, you moved on to the afterlife. Symbolically, the only thing "lighter than" (higher than) birds are sources of light like the sun, moon, and stars. It's all symbolic tips of the cap to having all chakras activated, i.e. being enlightened.
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npub1ncxn...29r0 7 months ago
Yes, it does map to the prisoners delimma now that you mention it. Specifically a Stockholm Syndrome prisoners delimma. A "no matter where you go, there you are" type of prison delimma.
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