Rohit Lamba
@rohitlamba.bsky.social
Economist, Himalayan boy, poetry enthusiast, foodie. Amor fati :)
www.rohitlamba.com
www.rohitlamba.com
18/ TL;DR: Adding a dash of noise (random experimentation) to learning dynamics, evolutionary reasoning can resolve (in many static games) equilibrium indeterminacy. The one with larger basin of attraction – the risk-dominant convention – tends to reign supreme in the long run.
July 29, 2025 at 4:20 AM
18/ TL;DR: Adding a dash of noise (random experimentation) to learning dynamics, evolutionary reasoning can resolve (in many static games) equilibrium indeterminacy. The one with larger basin of attraction – the risk-dominant convention – tends to reign supreme in the long run.
17/ A truly remarkable scholar of the field and whose book you must read is the late William H. Sandholm.
July 29, 2025 at 4:20 AM
17/ A truly remarkable scholar of the field and whose book you must read is the late William H. Sandholm.
16/ Intellectual history: Evolutionary game theory is inspired from biology’s idea of natural selection. John Maynard Smith (w/ G.R. Price) introduced the concept of Evolutionarily Stable Strategy (ESS) in 1973, showing how certain behaviors become stable in animal conflicts.
July 29, 2025 at 4:20 AM
16/ Intellectual history: Evolutionary game theory is inspired from biology’s idea of natural selection. John Maynard Smith (w/ G.R. Price) introduced the concept of Evolutionarily Stable Strategy (ESS) in 1973, showing how certain behaviors become stable in animal conflicts.
15/ Significance: KMR and Young bridged ideas from biology and bounded rationality to explain which social convention “wins” when everyone occasionally makes mistakes. The concept of stochastically stable equilibrium introduced here has become a key tool in economic theory.
July 29, 2025 at 4:20 AM
15/ Significance: KMR and Young bridged ideas from biology and bounded rationality to explain which social convention “wins” when everyone occasionally makes mistakes. The concept of stochastically stable equilibrium introduced here has become a key tool in economic theory.
14/ Beyond 2×2 games: Young showed the selected convention need not be the risk-dominant or Pareto-best. Nonetheless, his general algorithm can identify the stochastically stable convention in such cases. And more work has generalized the KMR techniques to general games as well.
July 29, 2025 at 4:20 AM
14/ Beyond 2×2 games: Young showed the selected convention need not be the risk-dominant or Pareto-best. Nonetheless, his general algorithm can identify the stochastically stable convention in such cases. And more work has generalized the KMR techniques to general games as well.
13/ The two papers--- KMR and Young have somewhat different setups, but they both eventually use Markov chain methods and results from perturbation theory (Freidlin–Wentzell).
July 29, 2025 at 4:20 AM
13/ The two papers--- KMR and Young have somewhat different setups, but they both eventually use Markov chain methods and results from perturbation theory (Freidlin–Wentzell).
12/ Young's method involves finding the minimum “cost” (fewest simultaneous mutations) needed to escape each equilibrium; the equilibrium with the highest escape cost is selected in the long run.
July 29, 2025 at 4:20 AM
12/ Young's method involves finding the minimum “cost” (fewest simultaneous mutations) needed to escape each equilibrium; the equilibrium with the highest escape cost is selected in the long run.
11/ Young’s result: By analyzing the “graph” of state transitions, he finds a unique stochastically stable equilibrium in many games. In 2×2 coordination games, it coincides with the risk-dominant convention – exactly as in KMR.
July 29, 2025 at 4:20 AM
11/ Young’s result: By analyzing the “graph” of state transitions, he finds a unique stochastically stable equilibrium in many games. In 2×2 coordination games, it coincides with the risk-dominant convention – exactly as in KMR.
10/ Even under adaptive play, multiple equilibria can persist (each is an absorbing convention if no one deviates). Young adds a small chance that players choose a non-best-response at random. Just as in KMR, these “mistakes” let some conventions prove more enduring than others.
July 29, 2025 at 4:20 AM
10/ Even under adaptive play, multiple equilibria can persist (each is an absorbing convention if no one deviates). Young adds a small chance that players choose a non-best-response at random. Just as in KMR, these “mistakes” let some conventions prove more enduring than others.
9/ Young introduces a boundedly rational learning rule: adaptive play. Population of players randomly matched to play a game; only remember a small sample of recent rounds; choose a best response to that. This limited memory (different for each player) prevents cyclic behavior.
July 29, 2025 at 4:20 AM
9/ Young introduces a boundedly rational learning rule: adaptive play. Population of players randomly matched to play a game; only remember a small sample of recent rounds; choose a best response to that. This limited memory (different for each player) prevents cyclic behavior.
8/ Risk dominance was introduced by Harsayni and Selten (1988): (G,G) here risk dominates (H,H) because the expected payoff from playing G is higher than H when you assume the other player is playing 50-50:
1/2* 4 + 1/2* 2 > 1/2* 5 + 1/2* 0.
So, (G,G) is the SSE.
1/2* 4 + 1/2* 2 > 1/2* 5 + 1/2* 0.
So, (G,G) is the SSE.
July 29, 2025 at 4:20 AM
8/ Risk dominance was introduced by Harsayni and Selten (1988): (G,G) here risk dominates (H,H) because the expected payoff from playing G is higher than H when you assume the other player is playing 50-50:
1/2* 4 + 1/2* 2 > 1/2* 5 + 1/2* 0.
So, (G,G) is the SSE.
1/2* 4 + 1/2* 2 > 1/2* 5 + 1/2* 0.
So, (G,G) is the SSE.
7/ KMR’s insight: In any 2×2 coordination game with 2 Nash equilibria, the risk-dominant equilibrium will prevail in the long run: it’s the equilib hardest to upset. If it takes a larger rare shock to leave Equilib A than to leave B, the system will spend most of its time at A.
July 29, 2025 at 4:20 AM
7/ KMR’s insight: In any 2×2 coordination game with 2 Nash equilibria, the risk-dominant equilibrium will prevail in the long run: it’s the equilib hardest to upset. If it takes a larger rare shock to leave Equilib A than to leave B, the system will spend most of its time at A.
6/ KMR analyze a finite population repeatedly playing a symmetric game. Successful strategies spread (Darwinian) and each player occasionally mutates (chooses a random action) instead of the best response. This ongoing noise “drastically reduces” the set of long-run equilibria.
July 29, 2025 at 4:20 AM
6/ KMR analyze a finite population repeatedly playing a symmetric game. Successful strategies spread (Darwinian) and each player occasionally mutates (chooses a random action) instead of the best response. This ongoing noise “drastically reduces” the set of long-run equilibria.
5/ Long-run equilib: Game never truly “freezes” at a NE, a tiny chance someone experiments. So process has a stationary distribution over states (what is played). As mutation probability → 0, distribution puts ~100% weight on a single stochastically stable equilibrium (SSE).
July 29, 2025 at 4:20 AM
5/ Long-run equilib: Game never truly “freezes” at a NE, a tiny chance someone experiments. So process has a stationary distribution over states (what is played). As mutation probability → 0, distribution puts ~100% weight on a single stochastically stable equilibrium (SSE).
4/ A dynamic approach: Instead of assuming players magically coordinate on an equilibrium, KMR/Young model how conventions emerge via a dynamic learning process with occasional random perturbations (small “mutations”). Players mostly adjust to success, but sometimes experiment.
July 29, 2025 at 4:20 AM
4/ A dynamic approach: Instead of assuming players magically coordinate on an equilibrium, KMR/Young model how conventions emerge via a dynamic learning process with occasional random perturbations (small “mutations”). Players mostly adjust to success, but sometimes experiment.
3/ Consider the Stag Hunt: In this coordination game, two pure Nash equilibria (NE) exist: (Hunt,Hunt) and (Gather,Gather). (Hunt,Hunt) is Pareto-best for both, but (Gather,Gather) is risk-dominant – it’s safer if you’re unsure what the other will do.
July 29, 2025 at 4:20 AM
3/ Consider the Stag Hunt: In this coordination game, two pure Nash equilibria (NE) exist: (Hunt,Hunt) and (Gather,Gather). (Hunt,Hunt) is Pareto-best for both, but (Gather,Gather) is risk-dominant – it’s safer if you’re unsure what the other will do.
2/ Just when you think you've understood all that Nash brought to game theory, he surprises you. This from his PhD thesis (1950), where he conceptualizes early on, how players could arrive at playing the (well, Nash) equilibrium: a population and an empirical perspective!
July 29, 2025 at 4:20 AM
2/ Just when you think you've understood all that Nash brought to game theory, he surprises you. This from his PhD thesis (1950), where he conceptualizes early on, how players could arrive at playing the (well, Nash) equilibrium: a population and an empirical perspective!
24/ On a personal note, I've learnt a lot about optimal taxation and particularly about the Atkinson-Stiglitz Theorem, its stark implications and its obvious practical limitations from @jacobsgoldin.bsky.social.
July 11, 2025 at 11:25 PM
24/ On a personal note, I've learnt a lot about optimal taxation and particularly about the Atkinson-Stiglitz Theorem, its stark implications and its obvious practical limitations from @jacobsgoldin.bsky.social.
23/ In practice: Atkinson-Stiglitz is a remarkable theoretical benchmark, not a blanket rule. Real-world tax systems do tax consumption (VAT, excises) and capital, because the theorem's assumptions often fail (preferences not separable, multiple sources of inequality, etc.).
July 11, 2025 at 11:25 PM
23/ In practice: Atkinson-Stiglitz is a remarkable theoretical benchmark, not a blanket rule. Real-world tax systems do tax consumption (VAT, excises) and capital, because the theorem's assumptions often fail (preferences not separable, multiple sources of inequality, etc.).
22/ Excellent recent work by Pai-@philippstrack.bsky.social, and Doligalski-Dworczak-Akbarpour- @skominers.bsky.social brings fresh perspectives on the Atkinson-Stiglitz theorem.
July 11, 2025 at 11:25 PM
22/ Excellent recent work by Pai-@philippstrack.bsky.social, and Doligalski-Dworczak-Akbarpour- @skominers.bsky.social brings fresh perspectives on the Atkinson-Stiglitz theorem.
21/ A-S remains a benchmark, but knowing when it fails is key for real-world tax design. These lectures by @s-stantcheva.bsky.social provide a great overview of how relaxing A-S assumptions shows when commodity or capital taxes become warranted. stantcheva.scholars.harvard.edu/sites/g/file...
July 11, 2025 at 11:25 PM
21/ A-S remains a benchmark, but knowing when it fails is key for real-world tax design. These lectures by @s-stantcheva.bsky.social provide a great overview of how relaxing A-S assumptions shows when commodity or capital taxes become warranted. stantcheva.scholars.harvard.edu/sites/g/file...
20/ @josephestiglitz.bsky.social critiques 0-capital-tax view. Notes A-S separability assump is implausible. In more realistic settings (imperfect info, inheritance, etc.), taxing capital can improve equity w/ acceptable efficiency costs.
[Though implementing inheritance taxes well has been hard.]
[Though implementing inheritance taxes well has been hard.]
July 11, 2025 at 11:25 PM
20/ @josephestiglitz.bsky.social critiques 0-capital-tax view. Notes A-S separability assump is implausible. In more realistic settings (imperfect info, inheritance, etc.), taxing capital can improve equity w/ acceptable efficiency costs.
[Though implementing inheritance taxes well has been hard.]
[Though implementing inheritance taxes well has been hard.]