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<p>&nbsp;There were great talks again on Day 2!&nbsp;</p><p><br /></p><p><b>Miloš Stojaković: "Strong Avoiding Positional Games"</b></p><p>Joint work with Jelena Stratijev.&nbsp; Positional games are played on a finite set X where the Winning Sets are given subsets.&nbsp; Players take turns claiming elements until all are taken.&nbsp; Then the winner is determined based on different classes of the positional games (e.g. the Strong Maker-Maker condition for Tic-Tac-Toe).&nbsp; Miloš talked about Strong Avoider-Avoider: the first player who claims an entire Winning Set (now the "losing set") loses.&nbsp; If no one does, then the game is a draw.</p><p>Sim, for example, is played on K_c with triangles as the Winning Sets.&nbsp; (Ramsey Theory tells us that a draw is not possible.)&nbsp; It turns out there is a winning strategy for the first player on 3^3 Tic-Tac-Toe!&nbsp; (The potential name Tic-Tac-No was mentioned.)&nbsp; No draws are possible here either.</p><p>Miloš's team found winning strategies for the second player for different Winning Sets of complete graphs.&nbsp; The proofs use a lot of cool techniques including strategy stealing!</p><p><br /></p><p><b>Daniella Popović: "A New Approach to Equivalence of Games"</b></p><p>Joint work with Nikola Milosavljević and Bojan Bašić.&nbsp; Daniella began by reminding us of the equivalence of games.&nbsp; She then presented a new idea: partitioning game DAGs into classes where two positions share a class if they all have options to the same other classes.&nbsp; This is called "Emulational Equivalence" and is flexible because it does not require knowledge of the play convention (Normal/Misere).&nbsp; Her team defined Hackenforb: players alternate deleting edges from a graph.&nbsp; If any component matches a forbidden set of subgraphs, it is also deleted.&nbsp;&nbsp;</p><p>Daniella then showed that Hackenforb and Nim are emulationally equivalent.&nbsp; They were also able to show equivalence from Hackenforb to Chomp!&nbsp; More importantly, they showed there are games that cannot be related to Hackenforb in this way!</p><p><br /></p><p><b>Michael Fisher: "Olympic Games: Three Impartial Games with Octal Codes"</b></p><p>Joint work with Keith Hazen and Craig Tennenhouse.&nbsp; Mike reminded us about Wythoff's Nim and Beatty sequences: using irrationals to define partitions on the natural numbers.&nbsp; He then reminded us about Octal Games, Kayles, Dawson's Chess, and Nim.&nbsp; Then Mike tied this in to Number Theory and Metallic Means: the Golden Ratio and Silver mean based on Pell Numbers.&nbsp; Bronze numbers exist as well, so Mike's team made an octal game based on each.&nbsp; E.g. the Golden Game uses the infinite octal code .1211212112112... (non-repeating!).&nbsp; The P-positions are at 0 = F1, F3, F5, F7, ...&nbsp; (the odd elements of the Fibonacci sequence).&nbsp; The Silver game does the same thing: each index is 1 or 2 depending on which side of the Silver-based Beatty sequences the index lands on.&nbsp; Mike showed graphs of Grundy values, but these did not reveal any obvious formulas.</p><p><b> </b><br /></p><p><b>Richard J Nowakowski: "The Game of Flipping Coins"</b></p><p>Joint work with Anthony Bonato and Melissa Huggan.&nbsp; This talk came about from teaching CGT to a non-CGT faculty member.&nbsp; They tried using Turning Turtles, but then wanted something to include partizan games as well.&nbsp; To do that they created Flipping Coins.&nbsp; This game is played on a string of 1s and 0s: Left can change two 1s into 0s (no matter what is between them) and Right can change a 0...1 to 1..0 (yes, the order matters).&nbsp; Thus, for example, the strings 11 = integer value 1 and 01 = -1.&nbsp; His group found integers and fractions.&nbsp; They discovered that Left has a serious advantage, but that all values are numbers.&nbsp; (That last bit uses the conditions from Alda's talk the previous day!)</p><p>It turns out that both players want to play usually at the right-end of the string, meaning it looks like the analysis could be related to ordinal sums.&nbsp; Richard's team found a complete way to evaluate positions!</p><p><br /></p><p><b>Tomoaki Abuku: "A Multiple Hook Removing Game Whose Starting Position is a Rectangular Young Diagram with Unimodal Numbering"</b></p><p>This is Joint Work with Masata Tada.&nbsp; In this new impartial game, the players play on a Young Diagram and remove one box and the corresponding hook: the boxes directly below and to the right.&nbsp; Then the remaining boxes are shifted up and to the left.&nbsp; This is a very interesting Chomp variant!&nbsp; Tomoaki then described a variant with a unimodal numbering on the boxes.&nbsp; After a move that removes a hook, the player <i>has to</i> go again if they can remove a book with the same multiset.&nbsp; This continues until no such matching multiset move exists.&nbsp; Tomoaki's team found a diagonal expression to classify positions, which they used to calculate many of the nimbers.&nbsp; Tomoaki described an equivalence to a version with shifted Young Diagrams that helped reduce game sizes.</p><p><br /></p><p><b>Kanae Yoshiwatari: "Complexity of Colored Arc Kayles"</b></p><p>Joint work with Tesshu Hanaka, Hironori Kiya, and Hirotaka Ono.&nbsp; Colored Arc Kayles is the partizan version of Arc Kayles where edges are colored by the player (or green/gray for either) who can play on that edge.&nbsp; Kanae reminded us about the relationship between Arc Kayles and Cram and Domineering.&nbsp; Kanae's team showed that Colored Arc Kayles is NP-hard, as well as some parameterized algorithms (still exponential) to solve it that improved on multiple previous results.&nbsp; Some of the parameters they use include the vertex cover and neighborhood diversity.</p><p><b> </b><br /></p><p><b>Eric Duchêne: "Partizan Subtraction Games"</b></p><p>Joint work with Marc Heinrich, Richard J Nowakowski, and Aline Parreau.&nbsp; Eric next presented his result on Partizan Subtraction games, which is just like impartial subtraction, but with separate subtraction sets.&nbsp; Eric's team showed that this game is NP-hard via a clever reduction from Generalized Knapsack.&nbsp; Then they showed the game is quite easy from some small sets and talked about the different styles of sequences of outcome classes.&nbsp; They showed that computing the length of the preperiod of the sequence is NP-hard using the Frobenius problem!&nbsp; Then they looked at the effects of set sizes between the players.</p><p><b> </b><br /></p><p><b>Aline Parreau: "Maker-Breaker Domination Game"</b></p><p>Joint work with:&nbsp;Guillaume Bagan, Eric Duchêne, Valentin Gledel, Tuomo Lehtilä, and Gabriel Renault.&nbsp; In this game, one player (the Maker) is trying to build a dominating set on the vertices of a graph while the other player tries to prevent that.&nbsp; Aline pointed out that you can swap the roles by thinking of the Breaker as trying to created closed neighborhoods.&nbsp; Aline's team showed that the game is PSPACE-complete, even for bipartite and split graphs.&nbsp; They also showed a property that implies a Maker win, then showed that the property is NP-hard to detect, but not in trees!&nbsp; Trees are one of few graph families Aline found to be solvable in Polynomial time.&nbsp; The hardness remains open for interval graphs.&nbsp; There are really interesting relationships between matchings.</p><p><b>&nbsp;</b></p><p><b>Hikaru Manabe: "Four-Dimensional Chocolate Games and Chocolate Games with a Pass Move"</b></p><p>Joint work with Aditi Singh, Yuki Tokuni, and Ryohei Miyadera.&nbsp; Hikaru is a high-school student in Japan!&nbsp; He spoke about Chomp games (on chocolate) but also using only horizontal and vertical cuts.&nbsp; His team looked at staircase functions that result in different board shapes and the nimbers you can get.&nbsp; Then Hikaru generalized to 3-d and then to 4-d!&nbsp; His team continued to use stair-shaped functions to grow boards out from the bitter (poison) square.&nbsp; Then they looked at the relationship with adding a pass move and how that could be modeled by shifting dimensions.<b> </b></p><p><br /></p><p>Amazing talks!&nbsp; Then we had a great conference dinner until way too late.&nbsp; (That's why these weren't out last night.)&nbsp; One more day to go!<br /></p>