This blog post explores how game theory can explain ancient debt inheritance practices. It argues that varying customs, like the complete forgiveness of debts upon death or the inheritance of debt by heirs, can be understood as strategic responses to different social and economic environments. Where strong social ties and community enforcement existed, debt forgiveness could be sustainable. Conversely, in societies with weaker community bonds, inheriting debt incentivized responsible lending and borrowing by holding both parties accountable, even beyond death. This system, akin to a repeated game in game theory, fostered trust and facilitated economic activity by increasing the likelihood of repayment.
The blog post "On Zero Sum Games (The Informational Meta-Game)" argues that while many real-world interactions appear zero-sum, they often contain hidden non-zero-sum elements, especially concerning information. The author uses poker as an analogy: while the chips exchanged represent a zero-sum component, the information revealed through betting, bluffing, and tells creates a meta-game that isn't zero-sum. This meta-game involves learning about opponents and improving one's own strategies, generating future value even within apparently zero-sum situations like negotiations or competitions. The core idea is that leveraging information asymmetry can transform seemingly zero-sum interactions into opportunities for mutual gain by increasing overall understanding and skill, thus expanding the "pie" over time.
HN commenters generally appreciated the post's clear explanation of zero-sum games and its application to informational meta-games. Several praised the analogy to poker, finding it illuminating. Some extended the discussion by exploring how this framework applies to areas like politics and social dynamics, where manipulating information can create perceived zero-sum scenarios even when underlying resources aren't truly limited. One commenter pointed out potential flaws in assuming perfect rationality and complete information, suggesting the model's applicability is limited in real-world situations. Another highlighted the importance of trust and reputation in navigating these information games, emphasizing the long-term cost of deceptive tactics. A few users also questioned the clarity of certain examples, requesting further elaboration from the author.
Transfinite Nim, a variation of the classic game Nim, extends the concept to infinite ordinal numbers. Players take turns removing any finite, positive number of stones from a single heap, but the heaps themselves can be indexed by ordinal numbers. The game proceeds as usual, with the last player to remove stones winning. The article explores the winning strategy for this transfinite game, demonstrating that despite the infinite nature of the game, a winning strategy always exists. This strategy involves considering the bitwise XOR sum of the heap sizes (using the Cantor normal form for ordinals) and aiming to leave a sum of zero after your turn. Crucially, the winning strategy requires a player to leave only finitely many non-empty heaps after each turn. The article further explores variations of the game, including when infinitely many stones can be removed at once, demonstrating different winning conditions in these altered scenarios.
HN commenters discuss the implications and interesting aspects of transfinite Nim. Several express fascination with the idea of games with infinitely many positions, questioning the practicality and meaning of "winning" such a game. Some dive into the strategy, mentioning the importance of considering ordinal numbers and successor ordinals. One commenter connects the game to the concept of "good sets" within set theory, while another raises the question of whether Zermelo-Fraenkel set theory is powerful enough to determine the winner for all ordinal games. The surreal number system is also brought up as a relevant mathematical structure for understanding transfinite games. Overall, the comments show a blend of curiosity about the theoretical nature of the game and attempts to grasp the strategic implications of infinite play.
The blog post explores using linear programming to optimize League of Legends character builds. It frames the problem of selecting items to maximize specific stats (like attack damage or ability power) as a linear program, where item choices are variables and stat targets are constraints. The author details the process of gathering item data, formulating the linear program, and solving it using Python libraries. They showcase examples demonstrating how this approach can find optimal builds based on desired stats, including handling gold constraints and complex item interactions like Ornn upgrades. While acknowledging limitations like the exclusion of active item effects and dynamic gameplay factors, the author suggests the technique offers a powerful starting point for theorycrafting and understanding item efficiency in League of Legends.
HN users generally praised the approach of using linear programming for League of Legends item optimization, finding it clever and interesting. Some expressed skepticism about its practical application, citing the dynamic nature of the game and the difficulty of accurately modeling all variables, like player skill and enemy team composition. A few pointed out existing tools that already offer similar functionality, like Championify and Probuilds, though the author clarified their focus on exploring the optimization technique itself rather than creating a fully realized tool. The most compelling comments revolved around the limitations of translating theoretical optimization into in-game success, highlighting the gap between mathematical models and the complex reality of gameplay. Discussion also touched upon the potential for incorporating more dynamic factors into the model, like build paths and counter-building, and the ethical considerations of using such tools.
Summary of Comments ( 1 )
https://news.ycombinator.com/item?id=43248993
Hacker News users discussed the practicality and cultural context of the debt settlement methods described in the linked article. Some questioned the realism of the scenarios presented, arguing that the proposed game theory model oversimplifies complex social dynamics and power imbalances of ancient societies. Others highlighted the importance of reputation and social capital in these pre-legal systems, suggesting that maintaining community trust was a more powerful motivator than the threat of ostracization presented in the game theory example. Several commenters pointed out similar historical examples of debt inheritance and social mechanisms for resolving them, drawing comparisons to practices in various cultures. There was also discussion about the effectiveness of ostracization as a punishment and how it compares to modern legal systems.
The Hacker News post titled "Game Theory and Settling the Debts of the Deceased in Ancient Times" (linking to a blog post on politicalcalculations.blogspot.com) has generated a modest discussion with a few interesting points.
One commenter highlights the complexity of inheritance laws throughout history, pointing out that primogeniture (the eldest son inheriting everything) was a relatively late development. They mention that earlier systems often involved complex divisions of property among heirs, potentially including daughters and other relatives, sometimes with specific items allocated to specific individuals. This commenter suggests that understanding these nuances is important for interpreting historical legal texts and practices related to debt and inheritance.
Another commenter focuses on the practicalities of debt enforcement in ancient societies, arguing that it would have been extremely difficult to collect debts from someone who had moved away or disappeared, especially in the absence of sophisticated record-keeping and communication systems. They suggest the blog post's game theory analysis might oversimplify the situation by assuming perfect information and enforceability.
A third commenter raises the issue of social reputation and its role in ensuring debt repayment. They contend that in tight-knit communities, the threat of reputational damage could have been a powerful motivator for heirs to honor their deceased relatives' debts, even without strict legal obligations. This perspective emphasizes the social and cultural context alongside the purely economic considerations presented in the blog post.
A final commenter briefly touches on the concept of "debt bondage," suggesting that in some ancient societies, unpaid debts could lead to enslavement of the debtor or their family members. This comment hints at the potentially severe consequences of debt in those times.
While the discussion thread isn't particularly extensive, it does offer some valuable perspectives that add nuance to the blog post's analysis. The commenters bring in important considerations related to historical inheritance practices, the practicalities of debt enforcement, the role of social reputation, and the potential for severe consequences like debt bondage.