Verbatica vs Game Theory

Meet Verbatica — an AI language trainer you can actually talk to. Learn English, Arabic, Chinese, or Russian by using the language, not just memorizing it: practice speaking, get your writing corrected, and chat freely whenever you want. Real progress comes from real practice — and Verbatica gives you a patient AI partner that's ready any time of day, with instant feedback on everything you say and write. Speak and get feedback Practice speaking out loud and let the AI listen. Get feedback on your pronunciation so you can be understood clearly — and build the confidence to actually talk, from your very first session. Write and get feedback Write in your new language and the AI checks your work on the spot. It points out each mistake and explains how to fix it, so every sentence you write moves you forward. Chat and ask anything Have a real conversation with your AI partner, or simply ask it your questions — a tricky grammar rule, the difference between two words, how to say something naturally. It's like having a language expert in your pocket, 24/7. Who is Verbatica for? For anyone learning English, Arabic, Chinese, or Russian who wants to move past textbook drills and start speaking with confidence — whether you're a complete beginner or sharpening advanced skills. Download Verbatica and start speaking with confidence, one conversation at a time.

Learn game theory and solve games step by step — with exact fractions, not rounded decimals. Game Theory: Nash Equilibrium is a course, a solver and a problem set in one app. Every answer comes with the reasoning behind it, so you can check your homework, prepare for an exam, or simply understand why people cooperate, compete and bluff. SOLVER — FOUR KINDS OF GAMES • Matrix games: 2 players with up to 6 strategies each, or 3 players with up to 3. Dominant strategies, iterated elimination, rationalizability, pure and mixed Nash equilibria, refinements, equilibrium selection, maximin, Pareto efficiency, Nash bargaining, Stackelberg commitment, repeated games, evolutionarily stable strategies and correlated equilibrium — 14 concepts in total. • Game trees: build a sequential game, add moves of chance, and solve it by backward induction. See which Nash equilibria rest on threats nobody would carry out. • Bayesian games: give one or both players private types and find the pure and mixed Bayesian Nash equilibria, checked type by type. • Cournot markets: 2 to 5 firms with known or private costs. Get best responses, the equilibrium, price, profits and consumer surplus, compared with a cartel, a Stackelberg leader and perfect competition — with the reaction curves drawn. LEARN — 24 TOPICS IN 6 UNITS From normal-form games and dominant strategies to mixed equilibria, subgame perfection, information sets, Bayesian games, signaling, auctions and continuous strategies. Each topic builds on the one before and includes a worked example computed by the same engine as the solver. PRACTICE — 31 CLASSIC PROBLEMS The Prisoner's Dilemma, Battle of the Sexes, Stag Hunt, Chicken, the tragedy of the commons, auctions, the Traveller's Dilemma and many more. Pick the equilibria yourself, get instant feedback, then study the full solution. WHY STUDENTS USE IT • Exact results: fractions such as 2/3 instead of 0.667, and all equilibria of two-player games, not just one. • Step by step: the method is shown, not only the answer. • 10 languages: English, Turkish, German, Spanish, French, Italian, Portuguese, Russian, Chinese and Japanese. • Lessons, solver and practice work offline (watching an ad needs a connection). No account, no banners. FREE TO TRY, ONE PURCHASE FOR EVERYTHING Lessons 1, 2 and 24 and two practice problems (the Prisoner's Dilemma and Chicken, with their solutions) are free, and so is the solver: without Full Access, each solve is unlocked by one short ad that you choose to watch. Full Access — a one-time in-app purchase, not a subscription — unlocks every lesson, ad-free solving and all 31 problems with their solutions. Made for students of economics, business, computer science and political science, in high school and at university, and for anyone curious about strategic thinking.