PCWorld reports that Microsoft's Copilot AI holds only 1.1% of the web AI market share, declining from 1.5% over the past year. ChatGPT dominates with 64.5% market share while Google's Gemini has grown to 21.5%, leaving Copilot far behind major competitors.

PCWorld reports that Mozilla's new CEO Anthony Enzor-DeMeo plans to integrate AI features into Firefox while maintaining user choice to disable them. This strategic shift addresses Firefox's stagnant market share and aims to compete with AI-centric browsers without compromising privacy principles. The optional AI implementation reflects Mozilla's commitment to transparency and user control in an increasingly competitive browser landscape. Mozilla recently confirmed that it's shifting gears and bringing AI features to its Firefox browser. However, according to the newly appointed CEO Anthony Enzor-DeMeo, the AI features will always be optional and possible to switch off completely.

We study the dynamics and equilibria of a new kind of routing games, where players - drivers of future autonomous vehicles - may switch between individual (HDV) and collective (CAV) routing. In individual routing, just like today, drivers select routes minimizing expected travel costs, whereas in collective routing an operator centrally assigns vehicles to routes. The utility is then the average experienced travel time discounted with individually perceived attractiveness of automated driving. The market share maximising strategy amounts to offering utility greater than for individual routing to as many drivers as possible. Our theoretical contribution consists in developing a rigorous mathematical framework of individualized collective routing and studying algorithms which fleets of CAVs may use for their market-share optimization. We also define bi-level CAV - HDV equilibria and derive conditions which link the potential marketing behaviour of CAVs to the behavioural profile of the human population. Practically, we find that the fleet operator may often be able to equilibrate at full market share by simply mimicking the choices HDVs would make. In more realistic heterogenous human population settings, however, we discover that the market-share maximizing fleet controller should use highly variable mixed strategies as a means to attract or retain customers. The reason is that in mixed routing the powerful group player can control which vehicles are routed via congested and uncongested alternatives. The congestion pattern generated by CAVs is, however, not known to HDVs before departure and so HDVs cannot select faster routes and face huge uncertainty whichever alternative they choose. Consequently, mixed market-share maximising fleet strategies resulting in unpredictable day-to-day driving conditions may, alarmingly, become pervasive in our future cities.

This paper examines the market for AI models in which firms compete to provide accurate model predictions and consumers exhibit heterogeneous preferences for model accuracy. We develop a consumer-firm duopoly model to analyze how competition affects firms' incentives to improve model accuracy. Each firm aims to minimize its model's error, but this choice can often be suboptimal. Counterintuitively, we find that in a competitive market, firms that improve overall accuracy do not necessarily improve their profits. Rather, each firm's optimal decision is to invest further on the error dimension where it has a competitive advantage. By decomposing model errors into false positive and false negative rates, firms can reduce errors in each dimension through investments. Firms are strictly better off investing on their superior dimension and strictly worse off with investments on their inferior dimension. Profitable investments adversely affect consumers but increase overall welfare.

Algorithmic collusion has emerged as a central question in AI: Will the interaction between different AI agents deployed in markets lead to collusion? More generally, understanding how emergent behavior, be it a cartel or market dominance from more advanced bots, affects the market overall is an important research question. We propose a hierarchical multi-agent reinforcement learning framework to study algorithmic collusion in market making. The framework includes a self-interested market maker (Agent~A), which is trained in an uncertain environment shaped by an adversary, and three bottom-layer competitors: the self-interested Agent~B1 (whose objective is to maximize its own PnL), the competitive Agent~B2 (whose objective is to minimize the PnL of its opponent), and the hybrid Agent~B$^\star$, which can modulate between the behavior of the other two. To analyze how these agents shape the behavior of each other and affect market outcomes, we propose interaction-level metrics that quantify behavioral asymmetry and system-level dynamics, while providing signals potentially indicative of emergent interaction patterns. Experimental results show that Agent~B2 secures dominant performance in a zero-sum setting against B1, aggressively capturing order flow while tightening average spreads, thus improving market execution efficiency. In contrast, Agent~B$^\star$ exhibits a self-interested inclination when co-existing with other profit-seeking agents, securing dominant market share through adaptive quoting, yet exerting a milder adverse impact on the rewards of Agents~A and B1 compared to B2. These findings suggest that adaptive incentive control supports more sustainable strategic co-existence in heterogeneous agent environments and offers a structured lens for evaluating behavioral design in algorithmic trading systems.

B.4 Complete set of experimental results associated to section 4 In this section we display the complete set of results associated to figures shown in section 4. We

The rapid advancement of LLMs sparked significant interest in their potential to augment or automate managerial functions. One of the most recent trends in AI benchmarking is performance of Large Language Models (LLMs) over longer time horizons. While LLMs excel at tasks involving natural language and pattern recognition, their capabilities in multi-step, strategic business decision-making remain largely unexplored. Few studies demonstrated how results can be different from benchmarks in short-term tasks, as Vending-Bench revealed. Meanwhile, there is a shortage of alternative benchmarks for long-term coherence. This research analyses a novel benchmark using a business game for the decision making in business. The research contributes to the recent literature on AI by proposing a reproducible, open-access management simulator to the research community for LLM benchmarking. This novel framework is used for evaluating the performance of five leading LLMs available in free online interface: Gemini, ChatGPT, Meta AI, Mistral AI, and Grok. LLM makes decisions for a simulated retail company. A dynamic, month-by-month management simulation provides transparently in spreadsheet model as experimental environment. In each of twelve months, the LLMs are provided with a structured prompt containing a full business report from the previous period and are tasked with making key strategic decisions: pricing, order size, marketing budget, hiring, dismissal, loans, training expense, R&D expense, sales forecast, income forecast The methodology is designed to compare the LLMs on quantitative metrics: profit, revenue, and market share, and other KPIs. LLM decisions are analyzed in their strategic coherence, adaptability to market changes, and the rationale provided for their decisions. This approach allows to move beyond simple performance metrics for assessment of the long-term decision-making.