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[Thread] What are some of your favourite learnings from Game Theory?

I would say the Nash Equilibrium for me. Essentially, It is a stable state of a system where no participant can gain by a change of strategy as long as all the other participants remain unchanged. Imagine if @BiryaniEnthu and @potatomato are captured by Grapevine. They are taken into two different rooms and given an option to confess or deny that they stole Grapes. The rules are as follows: 1. Both deny then, both can't use Grapevine for 2 days. 2. If @BiryaniEnthu confesses and @potatomato doesn't then, @BiryaniEnthu can't use Grapevine for 1 day but @potatomato can't use it for 10 days. 3. If @potatomato confesses and @BiryaniEnthu doesn't then, @potatomato can't use Grapevine for 1 day but @BiryaniEnthu can't use it for 10 days. 4. If both confess then, both can't use Grapevine for 3 days. So, what is the optimal strategy? Let's plot this as a matrix where b = BiryaniEnthu and p = potatomato ‎‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‏‏‎ ‎‎p confess‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎p deny b confess‏‏‎ ‎‏‏‎ ‎[[‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎3\3 ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎, ‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎1\10‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎], b deny‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎[[‏‏‎ ‎‏‏‎ ‎10\1 ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎,‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎2\2‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎]] For @BiryaniEnthu, if p confesses then, best option is to confess else they will get punished for 10 days. For @BiryaniEnthu, if p denies then, best option is to confess because they will get punished for 1 day only. Same applies for @potatomato, their best option is to confess too because of symmetry in the matrix. But did you notice one thing? When both confess, both will get 3 days punishment, which is the Nash Equilibrium state which is extremely stable as it covers downside risk. However, the global maxima for both was when both will deny it, so that both get 2 day punishment but this is an unstable state because it relies on the assumption that the other person will deny, especially when the other person knows that confessing will lead to a better outcome. Hence, there is a tension between individual rationality and group rationality. The Nash Equilibrium represents a situation where, despite the possibility of a better global outcome, the self-interest of each player leads them to a less optimal, but stable, outcome.

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Daily Series #2: Geeking out → Monte Carlo Simulations

I will continue with this series for people who like this kind of content, drop "+1" in the chat and I will tag you the next time I post content. Imagine you have a very complex situation with varying degrees of randomness. How do you evaluate the probability of certain outcomes? One way is a deterministic way which is to sit down and try to compute probabilities of events. Another way is to simulate these interactions with various seed values and see how these outcomes vary. This is called a Monte Carlo simulation, where we use random sampling to model and analyze complex systems that involve uncertainty. Let's set up a game and apply a Monte Carlo simulation to it. You(Hero) and Me(Villain) engage in a strategic coin flipping competition over a series of rounds. Before each round, both of us independently decide whether to flip a coin or pass the turn to the opponent. The outcomes are as follows: 1. If both players decide to flip, a fair coin is tossed, and the player who called it correctly gains a point. 2. If one player decides to flip and the other passes, the flipping player gains a point without the need for a coin toss. 3. If both players pass, no points are gained or lost. We can simulate it by making each decision random: 1. Hero and Villain both independently choose between 0 and 1 for deciding whether to toss or pass. We use 0 as Pass and 1 as Toss. 2. If both pass then we let the scores as is. 3. If one passes and not the other, then we add +1 to whoever decided to toss. 4. If both decide to toss then, we do a random coin flip where 0 = Heads and 1 = Tails. Hero can randomly choose between Heads or Tails. The Villain takes the opposite position. First is the Monte Carlo Simulation and the difference between potential outcomes for 1000 rounds and 20 simulations, which is the graph shared.

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