In game theory and multi-agent reinforcement learning (MARL), each agent selects a strategy, interacts with the environment and other agents, and subsequently updates its strategy based on the received payoff. This process generates a sequence of joint strategies $(s^t)_{t \geq 0}$, where $s^t$ represents the strategy profile of all agents at time step $t$. A widely adopted principle in MARL algorithms is "win-stay, lose-shift", which dictates that an agent retains its current strategy if it achieves the best response. This principle exhibits a fixed-point property when the joint strategy has become an equilibrium. The sequence of joint strategies under this principle is referred to as a satisficing path, a concept first introduced in [40] and explored in the context of $N$-player games in [39]. A fundamental question arises regarding this principle: Under what conditions does every initial joint strategy $s$ admit a finite-length satisficing path $(s^t)_{0 \leq t \leq T}$ where $s^0=s$ and $s^T$ is an equilibrium? This paper establishes a sufficient condition for such a property, and demonstrates that any finite-state Markov game, as well as any $N$-player game, guarantees the existence of a finite-length satisficing path from an arbitrary initial strategy to some equilibrium. These results provide a stronger theoretical foundation for the design of MARL algorithms.

With summer vacations still stretching off into the distance, taking advantage of Prime Day board game deals or snagging some discounted toys could be a very smart move. The WIRED Reviews team has a gaggle of kids of all ages between us, and most of us are still big kids at heart, so we've tried a lot of board games and toys over the years. Some of the best family board games are on sale for Prime Day. You can also find deals on some of the best STEM toys. I have handpicked a selection of WIRED-tested and -approved board games and toys right here, and I'll keep adding to this list during the Prime Days sales through July 11.

Game-theoretic models are effective tools for modeling multi-agent interactions, especially when robots need to coordinate with humans. However, applying these models requires inferring their specifications from observed behaviors -- a challenging task known as the inverse game problem. Existing inverse game approaches often struggle to account for behavioral uncertainty and measurement noise, and leverage both offline and online data. To address these limitations, we propose an inverse game method that integrates a generative trajectory model into a differentiable mixed-strategy game framework. By representing the mixed strategy with a conditional variational autoencoder (CVAE), our method can infer high-dimensional, multi-modal behavior distributions from noisy measurements while adapting in real-time to new observations. We extensively evaluate our method in a simulated navigation benchmark, where the observations are generated by an unknown game model. Despite the model mismatch, our method can infer Nash-optimal actions comparable to those of the ground-truth model and the oracle inverse game baseline, even in the presence of uncertain agent objectives and noisy measurements.

Given the deluge of bad news emanating from the games industry over the past 10 months, it was somewhat reassuring this weekend to sit in a crowd of 20,000 happy, passionate fans, watching the biggest event in the esports calendar: the League of Legends world championship finals. The event, at the O2 arena in London, was the culmination of a globetrotting five-week competition to discover the best team in the world. Never having attended before – mostly because the final is usually held in Asia, where the best players tend to come from – I wasn't really sure what to expect. Would I be able to follow what was happening? It turns out the answers to those questions were "sort of" and "hell, yes".

Playing strategy games is a challenging problem for artificial intelligence (AI). One of the major challenges is the large search space due to a diverse set of game components. In recent works, state abstraction has been applied to search-based game AI and has brought significant performance improvements. State abstraction techniques rely on reducing the search space, e.g., by aggregating similar states. However, the application of these abstractions is hindered because the quality of an abstraction is difficult to evaluate. Previous works hence abandon the abstraction in the middle of the search to not bias the search to a local optimum. This mechanism introduces a hyper-parameter to decide the time to abandon the current state abstraction. In this work, we propose a size-constrained state abstraction (SCSA), an approach that limits the maximum number of nodes being grouped together. We found that with SCSA, the abstraction is not required to be abandoned. Our empirical results on $3$ strategy games show that the SCSA agent outperforms the previous methods and yields robust performance over different games. Codes are open-sourced at \url{https://github.com/GAIGResearch/Stratega}.

But while the video game seemingly looks and plays much like other online strategy games, under the hood it's a very different story. That's because it doesn't rely on the servers running popular online strategy games like Eve Online and World of Warcraft. Instead, Dark Forest runs completely on a blockchain, in a way that means no one is in control of how it plays out. Its early success doesn't just reflect a fun way of making games that work in an entirely different way. It also helps prove that blockchains can be used for far more interesting and complex applications than just moving digital money around, something some blockchain boosters have been saying since the technology first emerged.

To put it simply, e-sport is just like sport, but virtual. To get an idea, this is more than'real' football and its 3.6 million practitioners. Except that the players, we do not see them, they are behind their screen, difficult to evaluate them. Then, we developed an artificial intelligence system that puts all this through a grinder, to assess each player, neutrally. Competitions are endowed with 2 million dollars for the winner, some players have a high-level athlete status, they train, including physically 8 hours a day.

Last March, Iowa State University mathematicians Leslie Hogben and Carolyn Reinhart received a welcome surprise. Adam Wagner, a postdoctoral fellow at Tel Aviv University, emailed to let them know he'd answered a question they'd published the week before -- though not by any of the usual math or brute-force computing techniques. Instead, he used a game-playing machine. "I was very happy to have the question answered. I was excited that Adam had done it with AI," said Hogben. Hogben and Reinhart's problem was one of four that Wagner solved using artificial intelligence.

While details on the three new games remain sparse, EA did offer some personnel info. Development on the new "Jedi" game will be headed by Stig Asmussen, who helmed the previous entry and, before that, Sony's "God of War III." The new first-person shooter, meanwhile, will be directed by Peter Hirschmann, who previously worked on numerous Star Wars games including "Star Wars: Battlefront" and "Star Wars: The Force Unleashed." The strategy game will be designed by a new studio formed by Greg Foertsch, a developer on the revered XCOM series of turn-based, sci-fi strategy games. Respawn Entertainment, creator of Titanfall and "Apex Legends," will lead development on the "Jedi" sequel and the shooter while handling production for the strategy game.

The last decade has seen an explosion in the popularity of board and card games that aren't just the traditional Christmas assortment. Families seeking interesting, actually fun alternatives to Monopoly and Trivial Pursuits have embraced the German-designed classics Catan and Carcassonne, as well as a growing range of exuberant, highly social card games exemplified by the irrepressible Exploding Kittens and the frighteningly timely Pandemic. And now, with successful, critically acclaimed video games such as Slay the Spire and Wildermyth drawing key design principles from board games, it's the perfect time to tempt the most stubborn console and PC owners away from their screens. Recently I asked video game designers on Twitter for their favourite board and card games to add to my own recommendations. Here then, are 10 examples worth investing in for the festive season, most aimed at teenagers and adults but all fabulously entertaining whether your players are veterans of Cluedo or Call of Duty.